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NCERT Solutions for Class 5 Maths Chapter 1 We the Travellers I (PDF) – 2027

NCERT Solutions for Class 5 Maths Chapter 1 We the Travellers I – step-by-step answers to every exercise and in-text question of the chapter, as per the latest NCERT syllabus for 2027. Read them online or download the free question-answer PDF.

Chapter 1 of Math Mela takes you on a journey — bullock carts, cycles, trains, ships and spacecraft — and uses that journey to open the door to five-digit numbers. You will learn to read, write, compare and round numbers up to 99,999, and finish with two clever puzzles: Mira’s subtraction trick and the King’s 20 horses.

NCERT Solutions for Class 5 Maths Chapter 1 We the Travellers I PDF

All the answers are on this page below. The PDF also explains every answer – why it is right and how to check it – so download it for revision.

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Solutions PDF (English medium)We the Travellers IView PDF
Solutions PDF (Hindi medium)हम हैं यात्री – 1View PDF

NCERT Solutions for Class 5 Maths Chapter 1 We the Travellers I – Questions and Answers

All 96 questions of the chapter (textbook pages 1 – 16) are answered below, in the order of the book – in-text questions, activities and the end-of-chapter exercises. Each answer is written the way you would write it in the exam.

In-text Questions — Page 1Opening page and Reading and writing large numbers

Q1When was the last time you went on a long trip? Where did you go? How did you travel? What was the duration of your trip? How much distance did you cover? Ask the elders who went with you to help you answer these questions.
Answer

This is about your own trip, so the answer is your own. Write five things: when, where, how you travelled, how long it took and how far it was.

Sample answer: Last December my family went from Jaipur to Delhi. We went by train. The train took about 5 hours. The distance is about 300 km.
Q2Do you know how many vehicles are currently there in your state?
Answer

Nobody can guess this correctly — it has to be looked up. The count runs into lakhs and crores, so it is a very big number.

Sample answer: Uttar Pradesh has more than 4 crore registered vehicles. That number has 8 digits. My state’s figure is ______ (fill in what you find).
Q3How do you write numbers to show several thousand objects?
Answer

We group the objects into thousands. Then we write how many thousands there are, followed by what is left over. For example, 7 thousands and 209 more are written as 7,209.

Q4Let us start with 1,000. What numbers do we get when we keep adding a thousand? [1,000] [2,000] [ ] [ ] [ ] [ ] [ ] [ ] [9,000]
Answer

Each new box is one thousand more than the box before it. The six empty boxes are:

1,000 → 2,000 → 3,000 → 4,000 → 5,000 → 6,000 → 7,000 → 8,000 → 9,000
Q5What number do we get when we add a thousand to 9,000? We get ten thousand. How do we write this number?
Answer

We write it as 10,000.

9,000 + 1,000 = 10,000 (read as ten thousand)

It has five digits — a 1 followed by four zeros.

In-text Questions — Page 2The place value chart and the Indian place value system

Q1Look at the table below and notice the pattern of writing numbers. In the place value chart, we have added another column, TTh. It stands for ten thousand. In the same way, 10 Thousands = Ten Thousand = 10,000.
×10×10×10×10TThThHTO110100100010000
The place value chart printed on page 2. Each place is ten times the place on its right.
Answer

The pattern is simple: each column is ten times the column on its right.

10 Ones = 1 Ten = 10
10 Tens = 1 Hundred = 100
10 Hundreds = 1 Thousand = 1,000
10 Thousands = 1 Ten Thousand = 10,000

So the chart now has five columns:

TThThHTO
1
10
100
1000
10000
Q2Do you remember how we read and write numbers in the Indian place value system? We use the same ten digits 0–9 in different places to write larger numbers. For example, 1,380 = 1 Thousand + 3 Hundreds + 8 Tens + 0 Ones. 9,123 = 9 Thousands + 1 Hundred + 2 Tens + 3 Ones.
Answer

Yes. We use only the ten digits 0–9. The place of a digit gives its value.

1 Thousand = 1,000
3 Hundreds = 300
8 Tens = 80
0 Ones = 0
1,000 + 300 + 80 + 0 = 1,380
9 Thousands = 9,000
1 Hundred = 100
2 Tens = 20
3 Ones = 3
9,000 + 100 + 20 + 3 = 9,123

In-text Questions — Pages 3–4Writing and naming numbers beyond 10,000 (token table)

Q1Page 3, row 5. Tokens: 10,000 + 10 + 10 + 10 + 1 + 1 + 1. Number Name: Ten thousand thirty-three. Fill in the Number and the digits in the TTh, Th, H, T and O columns.
Answer

The number is 10,033.

Step 1 — add up the tokens.

One 10,000 token = 10,000
Three 10 tokens = 30
Three 1 tokens = 3
10,000 + 30 + 3 = 10,033

Step 2 — put each digit in its column.

NumberTThThHTO
10,03310033
Q2Page 3, last row. Number: 10,458. Number Name: Ten thousand four hundred fifty-eight. Fill in the digits in the TTh, Th, H, T and O columns.
Answer

Read the number from the left, one digit to one column.

NumberTThThHTO
10,45810458
Q3Page 4, row 1. Tokens: 10,000 + 1,000 + 100 + 100 + 10 + 1 + 1 + 1 + 1. Digits given: TTh = 1, Th = 1, H = 2, T = 1, O = 4. Fill in the Number and the Number Name.
Answer

The number is 11,214, read as eleven thousand two hundred fourteen.

Step 1 — add up the tokens.

10,000
+ 1,000
+ 100 + 100 = 200
+ 10
+ 1 + 1 + 1 + 1 = 4
Total = 11,214

Step 2 — say the name. Split at the comma: 11 | 214.

11 thousand … 214 → eleven thousand two hundred fourteen
Q4Page 4, row 2. Number: 13,520. Number Name: Thirteen thousand five hundred twenty. Fill in the digits in the TTh, Th, H, T and O columns.
Answer
NumberTThThHTO
13,52013520

Check with the tokens:

One 10,000 + three 1,000 tokens = 13,000
Five 100 tokens = 500
Two 10 tokens = 20
13,000 + 500 + 20 = 13,520 ✓
Q5Page 4, row 3. Number: 20,000. Number Name: Twenty thousand. Fill in the digits in the TTh, Th, H, T and O columns.
Answer
NumberTThThHTO
20,00020000
Two 10,000 tokens = 10,000 + 10,000 = 20,000
Q6Page 4, row 4. Number: 45,867. Number Name: Forty-five thousand eight hundred sixty-seven. Fill in the digits in the TTh, Th, H, T and O columns.
Answer
NumberTThThHTO
45,86745867

Check with the tokens shown in the book:

Four 10,000 tokens = 40,000
Five 1,000 tokens = 5,000
Eight 100 tokens = 800
Six 10 tokens = 60
Seven 1 tokens = 7
40,000 + 5,000 + 800 + 60 + 7 = 45,867 ✓

Let Us Do — Page 5Question 1 — continuing number patterns

Let Us Do
Q11. Fill in the blanks by continuing the pattern in each of the following sequences. Discuss the patterns in class. (a)
456567678
Sequence (a) as printed on page 5 — three numbers are given and four boxes are empty.
Answer

Step 1 — find the jump. Take one number away from the next one.

567 – 456 = 111
678 – 567 = 111
So the rule is: add 111 each time.

The full chain:

456 → 567 → 678 → 789 → 900 → 1,011 → 1,122
Q21. (b) 1,050 → __ → 3,150 → 4,200 → __ → __ → __
Answer

Step 1 — find the jump. Use two numbers that are next to each other.

4,200 – 3,150 = 1,050
So the rule is: add 1,050 each time.
1,050 → 2,100 → 3,150 → 4,200 → 5,250 → 6,300 → 7,350
Q31. (c) 5,501 → 6,401 → 7,301 → __ → __ → __ → __
Answer

Step 1 — find the jump.

6,401 – 5,501 = 900
7,301 – 6,401 = 900
Rule: add 900 each time.
5,501 → 6,401 → 7,301 → 8,201 → 9,101 → 10,001 → 10,901
Q41. (d) 10,100 → 10,200 → 10,300 → __ → __ → __ → __ ↓ __ ← 10,900 ← __
Answer

Step 1 — find the jump.

10,200 – 10,100 = 100 → rule: add 100 each time.

Top row: 10,100 → 10,200 → 10,300 → 10,400 → 10,500 → 10,600 → 10,700
Bottom row (from the right box to the left box): 10,800 → 10,900 → 11,000

Q51. (e) 10,105 → 10,125 → __ → __ → __ → __ → __ ↓ __ ← __ ← __
Answer

Step 1 — find the jump.

10,125 – 10,105 = 20 → rule: add 20 each time.

Top row: 10,105 → 10,125 → 10,145 → 10,165 → 10,185 → 10,205 → 10,225
Bottom row (from the right box to the left box): 10,245 → 10,265 → 10,285

Q61. (f) 10,992 → 10,993 → __ → __ → __ → __ → __ ↓ __ ← __ ← __
Answer

Step 1 — find the jump.

10,993 – 10,992 = 1 → rule: add 1 each time.

Top row: 10,992 → 10,993 → 10,994 → 10,995 → 10,996 → 10,997 → 10,998
Bottom row (from the right box to the left box): 10,999 → 11,000 → 11,001

Q71. (g) 10,794 → 10,796 → 10,798 → __ → __ → __ → __ ↓ __ ← __ ← __
Answer

Step 1 — find the jump.

10,796 – 10,794 = 2
10,798 – 10,796 = 2 → rule: add 2 each time.

Top row: 10,794 → 10,796 → 10,798 → 10,800 → 10,802 → 10,804 → 10,806
Bottom row (from the right box to the left box): 10,808 → 10,810 → 10,812

Q81. (h) 73,005 → 72,004 → __ → __ → __ → __ → __ ↓ __ ← __ ← __
Answer

This chain goes down, not up.

Step 1 — find the jump.

73,005 – 72,004 = 1,001 → rule: take away 1,001 each time.

Top row: 73,005 → 72,004 → 71,003 → 70,002 → 69,001 → 68,000 → 66,999
Bottom row (from the right box to the left box): 65,998 → 64,997 → 63,996

Q91. (i) 82,350 → 83,350 → __ → __ → __ → __ → __ ↓ __ ← __ ← __
Answer

Step 1 — find the jump.

83,350 – 82,350 = 1,000 → rule: add 1,000 each time.

Top row: 82,350 → 83,350 → 84,350 → 85,350 → 86,350 → 87,350 → 88,350
Bottom row (from the right box to the left box): 89,350 → 90,350 → 91,350

Let Us Do — Pages 6–7Questions 2 to 5 — number names, order, comparing and digit swap

Let Us Do
Q12. Fill in the blanks appropriately. Use commas as required.
NumberNumber Name
8,045Eight thousand forty-five
7,209 
10,599 
 Ten thousand seven hundred forty-three
20,869Twenty thousand eight hundred sixty-nine
13,579 
 Ten thousand ten
 Fifty-six thousand four hundred ninety-one
45,045 
39,593 
50,005 
26,050 
81,200 
 Ninety thousand nine
 Twenty-three thousand two hundred thirty
 Thirty-six thousand one
The table printed on page 6. The empty cells are yours to fill.
Answer

Here is the whole table filled in. The orange cells are the ones you had to write.

NumberNumber Name
8,045Eight thousand forty-five
7,209Seven thousand two hundred nine
10,599Ten thousand five hundred ninety-nine
10,743Ten thousand seven hundred forty-three
20,869Twenty thousand eight hundred sixty-nine
13,579Thirteen thousand five hundred seventy-nine
10,010Ten thousand ten
56,491Fifty-six thousand four hundred ninety-one
45,045Forty-five thousand forty-five
39,593Thirty-nine thousand five hundred ninety-three
50,005Fifty thousand five
26,050Twenty-six thousand fifty
81,200Eighty-one thousand two hundred
90,009Ninety thousand nine
23,230Twenty-three thousand two hundred thirty
36,001Thirty-six thousand one
Q23. Arrange the numbers below in increasing order. You can use the number line below, if required.
40,34734,40740,47334,74073,40474,43047,34018,926020,00040,00060,00080,000
The eight numbers and the number line printed on page 6.
Answer

Increasing order means smallest first.

18,926 < 34,407 < 34,740 < 40,347 < 40,473 < 47,340 < 73,404 < 74,430
Q34. A student said 9,990 is greater than 49,014 because 9 is greater than 4. Is the student correct? Why or why not?
Answer

No, the student is not correct. 49,014 is the bigger number.

Step 1 — count the digits.

9,990 has 4 digits
49,014 has 5 digits
A 5-digit number is always bigger than a 4-digit number.

Step 2 — line them up in the place value chart.

TThThHTO
9,99009990
49,01449014

In the TTh column, 9,990 has nothing (0) and 49,014 has 4. So 49,014 wins straight away.

Q44. Use the number line below to find the position of the numbers. Fill in the blanks.
5,00010,00050,000
TThThHTO999049014You can use this place value chart to compare thenumbers.
The number line and the place value chart printed on page 7. Seven boxes are yours to fill.
Answer
10,000 – 5,000 = 5,000
So each box goes up by 5,000.
5,000 · 10,000 · 15,000 · 20,000 · 25,000 · 30,000 · 35,000 · 40,000 · 45,000 · 50,000

Where the two numbers sit:

  • 9,990 sits just before the 10,000 mark — only 10 short of it.
  • 49,014 sits just after the 45,000 mark, close to 50,000.
Q55. Digit swap. (a) In the number 1,478, interchanging the digits 7 and 4 gives 1,748. Now, interchange any two digits in the number 1,478 to make a number that is larger than 5,500.
Answer

Two swaps work. Either one is a correct answer.

Swap the 1 and the 7 : 1,478 → 7,418
Swap the 1 and the 8 : 1,478 → 8,471
Q65. (b) Interchange two digits of 10,593 to make a number i) Between 11,000 and 15,000. ii) More than 35,000.
Answer

The digits of 10,593, in order, are 1 · 0 · 5 · 9 · 3.

(i) Between 11,000 and 15,000 → 13,590

(ii) More than 35,000 → 50,193 (or 90,513)

Q75. (c) Interchange two digits of 48,247 to make a number i) As small as possible. ii) As big as possible.
Answer

The digits of 48,247, in order, are 4 · 8 · 2 · 4 · 7.

(i) As small as possible → 28,447

(ii) As big as possible → 84,247

Nearest Tens (10s), Hundreds (100s), and Thousands (1,000s) — Pages 7–8Nearest Tens (10s), Hundreds (100s), and Thousands (1,000s)

Q1The rabbit is at 2,346. Its food has been kept at its neighbouring tens. On which tens should the rabbit go to get its food, with the least number of steps?
Answer

The rabbit should go to 2,350.

2,3402,3462,350 6 steps back 4 steps forward
2,346 sits between 2,340 and 2,350. It is nearer to 2,350.

Step 1 — name the two neighbouring tens. They are 2,340 and 2,350.

Step 2 — measure the two distances.

2,346 – 2,340 = 6 steps
2,350 – 2,346 = 4 steps

Step 3 — pick the shorter one. 4 is less than 6, so the rabbit goes forward to 2,350, needing 4 jumps.

Q2The rabbit is at 2,346. Its food has been kept at its neighbouring hundreds. Which of the two hundreds should the rabbit go to? ______ is the nearest hundred of 2,346. It will need ______ jumps to reach ______.
Answer

2,300 is the nearest hundred of 2,346. It will need 46 jumps to reach 2,300.

2,3002,3462,400 2,350 (middle) 46 jumps back 54 jumps forward
2,346 is on the left half of the road from 2,300 to 2,400, so 2,300 is nearer.

Step 1 — name the two neighbouring hundreds. 2,300 and 2,400.

Step 2 — measure both distances.

2,346 – 2,300 = 46
2,400 – 2,346 = 54

Step 3 — pick the shorter one. 46 < 54, so the rabbit goes back to 2,300.

Q3The rabbit is at 2,346. Its food has been kept at its neighbouring thousands. Which number should the rabbit go to? ______ is the nearest thousand of 2,346. It will need ______ jumps to reach ______.
Answer

2,000 is the nearest thousand of 2,346. It will need 346 jumps to reach 2,000.

2,0002,3463,000 2,500 (middle) 346 jumps back 654 jumps forward
2,346 has not yet crossed the middle mark 2,500, so 2,000 is its nearest thousand.

Step 1 — name the two neighbouring thousands. 2,000 and 3,000.

Step 2 — measure both distances.

2,346 – 2,000 = 346
3,000 – 2,346 = 654

Step 3 — pick the shorter one. 346 < 654, so the rabbit goes back to 2,000.

Q4Fill in the boxes appropriately. Number / Nearest Tens / Nearest Hundreds / Nearest Thousands, for 3,176 · 4,017 · 5,789 · 8,203.
Answer
NumberNearest TensNearest HundredsNearest Thousands
3,1763,1803,2003,000
4,0174,0204,0004,000
5,7895,7905,8006,000
8,2038,2008,2008,000

Let Us Think — Pages 8–9Rounding off, and numbers that share the same neighbour

Let Us Think
Q11. Vijay rounded off a number to the nearest hundred. Suma rounded off the same number to the nearest thousand. Both got the same result. Circle the numbers they might have used. 7,126 · 7,835 · 7,030 · 6,999
Answer

Circle 7,030 and 6,999.

NumberVijay: nearest hundredSuma: nearest thousandSame?
7,1267,1007,000No
7,8357,8008,000No
7,0307,0007,000Yes ✓
6,9997,0007,000Yes ✓
Q22. Think and write two numbers that have the same — (a) Nearest ten. (For example, 19 and 21 have the same nearest ten, that is, 20.)
Answer

Sample answer: 71 and 73. Both have nearest ten 70.

71 → ones digit 1, which is less than 5 → nearest ten is 70
73 → ones digit 3, which is less than 5 → nearest ten is 70
Q32. (b) Nearest hundred.
Answer

Sample answer: 512 and 549. Both have nearest hundred 500.

512 → last two digits 12, less than 50 → nearest hundred is 500
549 → last two digits 49, less than 50 → nearest hundred is 500
Q42. (c) Nearest thousand.
Answer

Sample answer: 4,120 and 4,480. Both have nearest thousand 4,000.

4,120 → last three digits 120, less than 500 → nearest thousand is 4,000
4,480 → last three digits 480, less than 500 → nearest thousand is 4,000
Q53. Think and write the numbers that have the same — (a) Nearest ten and nearest hundred.
Answer

Sample answer: 302.

Nearest ten of 302 → ones digit 2, less than 5 → 300
Nearest hundred of 302 → last two digits 02, less than 50 → 300
Both are 300, so they match ✓
Q63. (b) Nearest hundred and nearest thousand.
Answer

Sample answer: 4,020.

Nearest hundred of 4,020 → last two digits 20, less than 50 → 4,000
Nearest thousand of 4,020 → last three digits 020, less than 500 → 4,000
Both are 4,000 ✓
Q73. (c) Nearest ten, hundred and thousand.
Answer

Sample answer: 5,002. All three roundings give 5,000.

Nearest ten → ones digit 2, less than 5 → 5,000
Nearest hundred → last two digits 02, less than 50 → 5,000
Nearest thousand → last three digits 002, less than 500 → 5,000

Let Us Do — Page 10Travelling, Now and Then — speed and how many vehicles

Let Us Do
Q11. A cyclist can cover 15 km in one hour. How much distance will she cover in 4 hours, if she maintains the same speed?
Answer

She will cover 60 km.

Distance in 4 hours = 4 × distance in 1 hour

4 × 15 = 60 km
Q22. A school has 461 girls and 439 boys. How many vehicles are needed for all of them to go on a trip using the following modes of travel? (a) Bicycle (2)
Answer

Step 1 — find the total number of children.

461 girls + 439 boys
461 + 439 = 900 children

Step 2 — one bicycle carries 2 people. Share 900 into groups of 2.

900 ÷ 2 = 450

Answer: 450 bicycles are needed.

Q32. (b) Autorickshaw (3)
Answer

Total children = 900. One autorickshaw carries 3.

900 ÷ 3 = 300

Answer: 300 autorickshaws.

Q42. (c) Car (4)
Answer

Total children = 900. One car carries 4.

900 ÷ 4
4 × 200 = 800, leaving 100
4 × 25 = 100, leaving 0
200 + 25 = 225

Answer: 225 cars.

Q52. (d) Big car (6)
Answer

Total children = 900. One big car carries 6.

900 ÷ 6
6 × 100 = 600, leaving 300
6 × 50 = 300, leaving 0
100 + 50 = 150

Answer: 150 big cars.

Q62. (e) Tempo traveller (10)
Answer

Total children = 900. One tempo traveller carries 10.

900 ÷ 10 = 90

Answer: 90 tempo travellers.

Q72. (f) Boat (20)
Answer

Total children = 900. One boat carries 20.

900 ÷ 20
20 × 40 = 800, leaving 100
20 × 5 = 100, leaving 0
40 + 5 = 45

Answer: 45 boats.

Q82. (g) Minibus (25)
Answer

Total children = 900. One minibus carries 25.

900 ÷ 25
25 × 20 = 500, leaving 400
25 × 16 = 400, leaving 0
20 + 16 = 36

Answer: 36 minibuses.

Q92. (h) Aeroplane (180)
Answer

Total children = 900. One aeroplane carries 180.

900 ÷ 180
180 × 5 = 900, leaving 0
So the answer is 5

Answer: 5 aeroplanes.

Finding Large Numbers Around Us — Pages 10–11Finding Large Numbers Around Us

Try This
Q1Find something in the textbook whose count is a 4-digit number.
Answer

A 4-digit number is anything from 1,000 to 9,999. Do not count one by one — estimate, which means make a careful guess using multiplication.

Sample answer: The number of words in this chapter.
One page has about 150 words. The chapter has 16 pages.
150 × 16 = 2,400 words — a 4-digit number.
Q2Now, let us try this with our school. (a) Our school has ________ classrooms.
Answer

This is about your own school, so go and count.

Sample answer: Our school has 12 classrooms — 5 on the ground floor and 7 on the first floor.
Q3(b) There are ________ students in my class.
Answer

Count the children in your own classroom.

Sample answer: My class has 38 students — 6 rows of 6, and 2 more children on the last bench. 6 × 6 = 36, and 36 + 2 = 38.
Q4(c) Our classroom has ________ books in total.
Answer

Count all the books in the room — textbooks, notebooks and library books.

12 books × 38 children = 456
456 + 44 books in the cupboard = 500 books
Sample answer: Our classroom has about 500 books in total.
Q5Find something in the classroom whose count is a — (i) 4-digit number. (ii) 5-digit number.
Answer
Q6List some quantities whose count is a 4-digit or a 5-digit number in the context of — (i) A tree.
Answer

Take a full-grown mango tree in the village.

What we countRough countHow many digits
Mangoes on the tree in one seasonabout 1,5004-digit
Leaves on the treeabout 25,0005-digit
Seeds dropped in a yearabout 1,5004-digit
Days the tree has been alive (about 15 years)about 5,4754-digit
Q7List some quantities whose count is a 4-digit or a 5-digit number in the context of — (ii) Your village/town/city, or any other place of your choice.
Answer

Choose your own village or town and fill in real figures where you can. Here is a filled-in example.

What we countRough countHow many digits
People living in the villageabout 4,8004-digit
Houses in the villageabout 1,1004-digit
People living in a small townabout 45,0005-digit
Two-wheelers in the townabout 12,0005-digit
Trees along the town roadsabout 3,0004-digit
Students in all the schools of the townabout 10,5005-digit

Pastime Mathematics — Pages 11–13Pastime Mathematics — Sanju and Mira’s puzzles on the train

Try ThisMath Talk
Q11. Mira poses the river crossing puzzle to Sanju. A boatman wants to cross a river in a boat. He has to take a lion, a sheep, and a bundle of grass with him. He can take one of them at a time. If the sheep and grass are left on the shore, the sheep will eat the grass. And, if the sheep and lion are left on the shore, the lion will eat the sheep. How can the boatman take the lion, sheep, and grass across the river? Help him so that he can ferry the lion, sheep, and grass across the river safely, and in the minimum number of trips.
grasslionsheepboatmanRiver
The river crossing puzzle. The grass, the lion and the sheep are all on this bank; the boatman must take them across, one at a time.
Answer

It can be done in 7 trips. The trick is that the boatman is allowed to bring something back.

TripWhat the boatman doesLeft behind on this sideWaiting on the far side
1Takes the sheep acrosslion, grasssheep
2Comes back alonelion, grasssheep
3Takes the grass acrosslionsheep, grass
4Brings the sheep backlion, sheepgrass
5Takes the lion acrosssheeplion, grass
6Comes back alonesheeplion, grass
7Takes the sheep across—lion, sheep, grass

Check every stage. The lion and the sheep are never left alone together. The sheep and the grass are never left alone together. So nothing gets eaten.

Q22. Sanju introduces a game called pile of pebbles to Mira. There are two piles of pebbles. Each pile contains 7 pebbles. Each player can pick as many pebbles they want from either of the piles. The player who picks the last pebble wins. Try this game with your friends. Now, how do you play so that you win? To find a winning strategy, try playing with 1 pebble in each pile, two in each, three in each, and so on.
Answer

Play second, and always make the two piles equal again. Do that every turn and you will win.

Let the other player go first.
Whatever they take from one pile, take exactly the same number from the other pile.
The piles are equal after every one of your turns.
Q33. Now, it’s Mira’s turn. She gives a fun puzzle to Sanju: (a) Take any two different digits. (b) Make two 2-digit numbers using them. (c) Subtract the smaller number from the bigger number. Now, use the two digits in the difference and repeat steps (b) and (c). Continue until you get a 1-digit number. Mira exclaimed, No matter which two numbers you choose, you will get 9 in the end. How did Mira know what the 1-digit number in the end would be?
Answer

Mira knew because every difference you can ever get is a number in the 9 times table, and the chain of 9s always ends at 9 itself.

Difference of the numbers = 9 × (difference of the two digits)
Here: 7 – 3 = 4, and 9 × 4 = 36 ✓
Q4(1) Observe the differences you get in each step above. Do you notice anything in common?
73−373663−362772−274554−459
The whole process for the digits 3 and 7, as printed in the book.
Answer

The differences in the book’s example are 36, 27, 45, 9. Two things are true of every one of them.

  1. Each one is in the 9 times table.
  2. The digits of each one add up to 9.
DifferenceIs it 9 × something?Digits added
369 × 43 + 6 = 9
279 × 32 + 7 = 9
459 × 54 + 5 = 9
99 × 19
Q5(2) Try the puzzle using any other pair of digits. What is common to these differences? What do you get in the end?
For example(a)Take any two different digits.3 and 7(b)Make two 2-digit numbersusing them.37 and 73(c)Subtract the smaller numberfrom the bigger number.73 – 37 = 36Now use the two digits in the difference andrepeat steps (b) and (c).
The steps of Mira’s puzzle, with the book’s worked example beside them.
Answer

Take the digits 2 and 9.

Step 1 : 92 – 29 = 63
Step 2 : 63 – 36 = 27
Step 3 : 72 – 27 = 45
Step 4 : 54 – 45 = 9

What is common: every difference is a multiple of 9 — 63, 27, 45, 9. And you always end at 9, however many steps it takes.

Q6(3) What digits can you choose so that you get a 1-digit number in the first step itself? Give some examples. Describe the pattern in the digits.
For example(a)Take any two different digits.3 and 7(b)Make two 2-digit numbersusing them.37 and 73(c)Subtract the smaller numberfrom the bigger number.73 – 37 = 36Now use the two digits in the difference andrepeat steps (b) and (c).
The steps of Mira’s puzzle, with the book’s worked example beside them.
Answer

Choose two digits that are next-door neighbours — digits that differ by 1.

Examples:
2 and 3 → 32 – 23 = 9
4 and 5 → 54 – 45 = 9
6 and 7 → 76 – 67 = 9
8 and 9 → 98 – 89 = 9

The pattern: the two digits are consecutive — one is exactly 1 more than the other.

Q7(4) Now, find different digits such that the difference between the numbers is 27.
Answer

Choose two digits that are 3 apart.

Why 3? Because difference of numbers = 9 × (difference of digits)
27 = 9 × 3, so the digits must differ by 3.

All the pairs that work:

DigitsThe two numbersSubtraction
1, 441 and 1441 – 14 = 27
2, 552 and 2552 – 25 = 27
3, 663 and 3663 – 36 = 27
4, 774 and 4774 – 47 = 27
5, 885 and 5885 – 58 = 27
6, 996 and 6996 – 69 = 27
Q8(5) Mira found an interesting relationship between the two digits and the difference obtained. Can you see it in the table that Mira made?
DigitsDifferences in digitsDifference in numbers formed by the digits
3, 77 – 3 = 473 – 37 = 36
1, 99 – 1 = 891 – 19 = 72
2, 88 – 2 = 682 – 28 = 54
4, 55 – 4 = 154 – 45 = 9
The table Mira made, printed on page 13.
Answer

Yes. The relationship is:

Difference in the numbers = 9 × Difference in the digits

Check it on every row of Mira’s table.

DigitsDifference in digits9 × thatDifference in numbers
3, 749 × 4 = 3673 – 37 = 36 ✓
1, 989 × 8 = 7291 – 19 = 72 ✓
2, 869 × 6 = 5482 – 28 = 54 ✓
4, 519 × 1 = 954 – 45 = 9 ✓
Q9Extend this table by choosing appropriate digits so that the resulting differences are 2, 3, 5, and 7 respectively.
DigitsDifferences in digitsDifference in numbers formed by the digits
3, 77 – 3 = 473 – 37 = 36
1, 99 – 1 = 891 – 19 = 72
2, 88 – 2 = 682 – 28 = 54
4, 55 – 4 = 154 – 45 = 9
   
   
   
   
The table Mira made, printed on page 13, with four empty rows for you to add.
Answer

Mira’s table already covers digit differences 4, 8, 6 and 1. The four missing ones are 2, 3, 5 and 7. Here they are.

DigitsDifference in digitsDifference in the numbers formed
3, 55 – 3 = 253 – 35 = 18
1, 44 – 1 = 341 – 14 = 27
2, 77 – 2 = 572 – 27 = 45
1, 88 – 1 = 781 – 18 = 63
Q10What do the differences between the digits indicate?
Answer

The difference between the two digits tells you which multiple of 9 you will get. Multiply it by 9.

Difference in digits12345678
Difference in numbers918273645546372

So the digit difference is like a code number. Once you know it, you know the answer without subtracting at all.

Q11List the numbers that give a 1-digit number in the third subtraction.
Answer

You reach 9 on the third subtraction when your two digits are 3 apart or 8 apart.

The numbers are: 41 and 14 · 52 and 25 · 63 and 36 · 74 and 47 · 85 and 58 · 96 and 69.

The numbers are: 91 and 19.

Q12Identify pairs of digits that lead to the 1-digit number after the maximum possible number of subtractions. Compare your answers with your friends.
Answer

The longest possible chain takes 5 subtractions. It happens when the two digits are exactly 2 apart.

The pairs: (1, 3) · (2, 4) · (3, 5) · (4, 6) · (5, 7) · (6, 8) · (7, 9).

Let Us Do — Pages 13–15Questions 1 to 9 — writing numbers in between, ordering, expanded form and counting notes

Let Us Do
Q11. Write 5 numbers between the numbers 23,568 and 24,234.
Answer

Sample answer: 23,600 · 23,750 · 23,900 · 24,000 · 24,150

23,568 < 23,600 < 23,750 < 23,900 < 24,000 < 24,150 < 24,234
Q22. Write 5 numbers that are more than 38,125 but less than 38,600.
Answer

Sample answer: 38,200 · 38,300 · 38,400 · 38,500 · 38,550

38,125 < 38,200 < 38,300 < 38,400 < 38,500 < 38,550 < 38,600
Q33. Ravi’s car has been driven for 56,987 km till now. Sheetal’s car has been driven 67,543 km. Whose car has been driven more?
Answer

Sheetal’s car has been driven more.

Step 1 — count the digits. Both numbers have 5 digits, so we must compare place by place.

Step 2 — start from the left.

TThThHTO
Ravi 56,98756987
Sheetal 67,54367543
In the TTh column: 6 is more than 5
So 67,543 > 56,987 → Sheetal’s car
Q44. The following are the prices of different electric bikes. Arrange the prices in ascending (increasing) order. ₹90,000 · ₹89,999 · ₹94,983 · ₹49,900 · ₹93,743 · ₹39,999
Answer

Ascending order means cheapest first.

₹39,999 < ₹49,900 < ₹89,999 < ₹90,000 < ₹93,743 < ₹94,983
Q55. The following table shows the population of some towns. Arrange them in a descending (decreasing) order.
TownPopulation
Town 165,232
Town 253,231
Town 356,380
Town 451,336
Town 545,858
Town 666,540
The population table printed on page 14.
Answer

Descending order means biggest first.

66,540 > 65,232 > 56,380 > 53,231 > 51,336 > 45,858
PlaceTownPopulation
1st (largest)Town 666,540
2ndTown 165,232
3rdTown 356,380
4thTown 253,231
5thTown 451,336
6th (smallest)Town 545,858
Q66. Find numbers between 42,750 and 53,500 such that the ones, tens, and hundreds digits are all 0.
Answer

There are 11 such numbers:

43,000 · 44,000 · 45,000 · 46,000 · 47,000 · 48,000 · 49,000 · 50,000 · 51,000 · 52,000 · 53,000
Q77. Write the following numbers in the expanded form. One has been done for you: (a) 783 = 700 + 80 + 3. (b) 8,062 =
Answer

8,062 = 8,000 + 60 + 2

ThHTO
8062
8 in the thousands place = 8,000
0 in the hundreds place = 0
6 in the tens place = 60
2 in the ones place = 2
Q87. (c) 9,980 =
Answer

9,980 = 9,000 + 900 + 80

9 thousands = 9,000
9 hundreds = 900
8 tens = 80
0 ones = 0
9,000 + 900 + 80 = 9,980 ✓
Q97. (d) 10,304 =
Answer

10,304 = 10,000 + 300 + 4

TThThHTO
10304
1 ten thousand = 10,000
0 thousands = 0
3 hundreds = 300
0 tens = 0
4 ones = 4
10,000 + 300 + 4 = 10,304 ✓
Q107. (e) 23,004 =
Answer

23,004 = 20,000 + 3,000 + 4

2 ten thousands = 20,000
3 thousands = 3,000
0 hundreds = 0
0 tens = 0
4 ones = 4
20,000 + 3,000 + 4 = 23,004 ✓
Q117. (f) 70,405 =
Answer

70,405 = 70,000 + 400 + 5

TThThHTO
70405
7 ten thousands = 70,000
4 hundreds = 400
5 ones = 5
70,000 + 400 + 5 = 70,405 ✓
Q128. Fill in the blanks with the correct answer. Share your thoughts in class. (a) 983 = 90 Tens + 83 Ones. (b) 68 = ___ Tens + 18 Ones
Answer

68 = 5 Tens + 18 Ones

18 Ones = 18
68 – 18 = 50
50 = 5 Tens → the blank is 5

Check: 5 Tens + 18 Ones = 50 + 18 = 68 ✓

Q138. (c) 607 = 4 Hundreds + ___ Ones
Answer

607 = 4 Hundreds + 207 Ones

4 Hundreds = 400
607 – 400 = 207
207 = 207 Ones → the blank is 207

Check: 400 + 207 = 607 ✓

Q148. (d) 5,621 = 4 Thousand + ___ Hundreds + 2 Tens + ___ Ones
Answer

5,621 = 4 Thousand + 16 Hundreds + 2 Tens + 1 One

4 Thousand = 4,000
2 Tens = 20
5,621 – 4,000 – 20 = 1,601
1,601 = 1,600 + 1
1,600 = 16 Hundreds
1 = 1 One

Check: 4,000 + 1,600 + 20 + 1 = 5,621 ✓

Q158. (e) 7,069 = ___ Thousand + 20 Hundreds + ___ Ones
Answer

7,069 = 5 Thousand + 20 Hundreds + 69 Ones

20 Hundreds = 20 × 100 = 2,000
7,069 – 2,000 = 5,069
5,069 = 5,000 + 69
5,000 = 5 Thousand
69 = 69 Ones

Check: 5,000 + 2,000 + 69 = 7,069 ✓

Q168. (f) 37,608 = ___ Ten Thousand + 17 Thousand + ___ Hundreds + 8 Ones
Answer

37,608 = 2 Ten Thousand + 17 Thousand + 6 Hundreds + 8 Ones

17 Thousand = 17,000
8 Ones = 8
37,608 – 17,000 – 8 = 20,600
20,600 = 20,000 + 600
20,000 = 2 Ten Thousand
600 = 6 Hundreds

Check: 20,000 + 17,000 + 600 + 8 = 37,608 ✓

Q178. (g) 43,001 = 3 Ten Thousand + ____ Thousand + ____ Hundreds + 1 Ones
Answer

43,001 = 3 Ten Thousand + 13 Thousand + 0 Hundreds + 1 One

3 Ten Thousand = 30,000
1 One = 1
43,001 – 30,000 – 1 = 13,000
13,000 = 13 Thousand and no hundreds
Thousands blank = 13, Hundreds blank = 0

Check: 30,000 + 13,000 + 0 + 1 = 43,001 ✓

Q189. Fill in the blanks with the correct answers. (a) How many notes of ₹10 are there in ₹7,934? — 793. (b) How many notes of ₹100 are there in ₹7,934?
Answer

79 notes of ₹100.

7,934 ÷ 100
7,900 ÷ 100 = 79, and ₹34 is left over
So there are 79 notes of ₹100, with ₹34 left over.
Q199. (c) How many thousands are there in 7,934?
Answer

7 thousands.

7,934 ÷ 1,000
7,000 ÷ 1,000 = 7, and 934 is left over
So there are 7 thousands, with 934 left over.
Q209. (d) How many ₹500 notes are there in ₹7,934? (Hint: Observe the answer of (iii))
Answer

15 notes of ₹500 (with ₹434 left over).

Use the hint. Part (c) told us that ₹7,934 holds 7 thousands.

₹1,000 = two ₹500 notes
7 thousands → 7 × 2 = 14 notes of ₹500 (that is ₹7,000)
7,934 – 7,000 = 934
934 is more than 500, so one more ₹500 note fits
14 + 1 = 15 notes
Q219. (e) How many notes of ₹10 are there in ₹65,342?
Answer

6,534 notes of ₹10 (with ₹2 left over).

65,342 ÷ 10
65,340 ÷ 10 = 6,534, and ₹2 is left over

The quick way: Cover the last digit of 65,342. What remains is 6,534.

Q229. (f) How many notes of ₹100 are there in ₹65,342?
Answer

653 notes of ₹100 (with ₹42 left over).

65,342 ÷ 100
65,300 ÷ 100 = 653, and ₹42 is left over

The quick way: Cover the last two digits of 65,342. What remains is 653.

Q239. (g) How many thousands are there in 65,342?
Answer

65 thousands (with 342 left over).

65,342 ÷ 1,000
65,000 ÷ 1,000 = 65, and 342 is left over

The quick way: Cover the last three digits of 65,342. What remains is 65.

Q249. (h) How many ₹500 notes are there in ₹65,342?
Answer

130 notes of ₹500 (with ₹342 left over).

Use part (g). ₹65,342 holds 65 thousands.

65 × 2 = 130 notes of ₹500 (that is ₹65,000)
65,342 – 65,000 = 342
342 is less than 500, so no extra note fits

King’s Horses — Pages 15–16King’s Horses

Try ThisMath Talk
Q1But wait, were there really 20 horses in the stable? Count the horses one by one and check!
The dots show how the horses were arranged in the stable.
Answer

No. There were only 19 horses. One had already been stolen.

Count the rooms one by one:

Top wall : 1 + 2 + 2 + 0 = 5
Left wall (middle rooms) : 1 + 3 = 4
Right wall (middle rooms) : 2 + 3 = 5
Bottom wall : 0 + 2 + 3 + 0 = 5
5 + 4 + 5 + 5 = 19 horses
Q2What was the mistake in the caretaker’s explanation?
Answer

The caretaker counted the corner rooms twice.

4 sides × 5 horses = 20 counts
But the corner horses got counted twice.
The corner rooms hold 1 + 0 + 0 + 0 = 1 horse.
20 – 1 = 19 horses ✓
Q3The following night, the thief stole another horse from the stable. Now, only 18 horses remained. The caretaker once again cleverly arranged the 18 horses, so that there were 5 horses on each side of the square stable. How do you think he was able to do it? Arrange the 18 horses in the stable with 5 on each side.
The square stable: 4 rooms along each side, with an open yard in the middle.
Answer

He moved more horses into the corner rooms. The more horses sit in corners, the more often they get counted twice, and the fewer horses he needs in total.

Here is one arrangement of 18 horses with 5 on every side.

18 horses, 5 along every side. The two top corners now hold 1 horse each.
Q4How many more horses can the thief steal before the king notices something is wrong? Try making the arrangements yourself.
The square stable: 4 rooms along each side, with an open yard in the middle.
Answer

8 more horses. The caretaker can keep up the trick until only 10 horses are left.

Here is that arrangement.

The smallest possible stable: only 10 horses, yet still 5 along every side.
Horses now = 18
Fewest possible = 10
18 – 10 = 8 more horses can be stolen

Chapter 1 of 15 – Maths

Also for This Chapter

NCERT Solutions Class 5 Maths Chapter 1 We the Travellers I – Overview

ClassClass 5
SubjectMaths
Chapter1 – We the Travellers I
Textbook pages1 – 16
Questions solved96
Session2027
FormatFull answers on this page + PDF

NCERT Solutions Class 5 Maths Chapter 1 – FAQs

Where can I download NCERT Solutions Class 5 Maths Chapter 1 We the Travellers I PDF?

Read every answer on this page, or download the free PDF from the table at the top.

Is this for the 2027 session?

Yes, it follows the latest NCERT Class 5 Maths book for 2027.

How many questions are solved in NCERT Class 5 Maths Chapter 1?

All 96 questions of the chapter (textbook pages 1 – 16) – the in-text questions, activities and the end-of-chapter exercises.

How should I use these solutions?

Read the chapter in the NCERT book first, attempt the questions yourself, then check your answers here.

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