NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 – 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 7 closes Ganita Prakash Part I. It opens with five resized copies of the same photograph of a tiger and asks a question you can answer by eye but not yet by arithmetic — why do three of them look right and two look stretched? The answer is the ratio: a shape survives resizing only when every measurement is multiplied by the same factor. From that one idea the chapter builds proportion, cross multiplication, the ancient Trairasika (Rule of Three), sharing a quantity in a given ratio, and unit conversion.
NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 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.
| Chapter | Download | |
|---|---|---|
| Solutions PDF (English medium) | Proportional Reasoning 1 | View PDF |
| Solutions PDF (Hindi medium) | समानुपातिक तर्कण-1 | View PDF |
NCERT Solutions for Class 8 Maths Chapter 7 Proportional Reasoning 1 – Questions and Answers
All 69 questions of the chapter (textbook pages 159 – 177) 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 — Pages 159–1607.1 Observing Similarity in Change
Images A, C and D look similar. Images B and E look different — even though every one of the five shows the same tiger.
C → 30 mm × 20 mm → 3 : 2
D → 90 mm × 60 mm → 3 : 2
B → 40 mm × 20 mm → 2 : 1
E → 60 mm × 60 mm → 1 : 1
No. They are distorted. In B the tiger appears stretched and elongated; in E it appears compressed and fatter.
E → 60 : 60 = 1 : 1 (not wide enough for its height)
Because in B and E the width and the height were not changed by the same factor.
A → E : width 60 → 60, factor 1 ; height 40 → 60, factor 60⁄40 = 3⁄2
In each case the two factors are different, so one direction was stretched more than the other.
| Image | Width (in mm) | Height (in mm) |
|---|---|---|
| Image A | 60 | 40 |
| Image B | 40 | 20 |
| Image C | 30 | 20 |
| Image D | 90 | 60 |
| Image E | 60 | 60 |
A, C and D were obtained from one another by multiplying both the width and the height by the same factor. B and E were not.
| From A to | Width factor | Height factor | Same? |
| C (30 × 20) | 30⁄60 = 1⁄2 | 20⁄40 = 1⁄2 | Yes — similar |
| D (90 × 60) | 90⁄60 = 3⁄2 | 60⁄40 = 3⁄2 | Yes — similar |
| B (40 × 20) | 40⁄60 = 2⁄3 | 20⁄40 = 1⁄2 | No — distorted |
| E (60 × 60) | 60⁄60 = 1 | 60⁄40 = 3⁄2 | No — distorted |
| Image | Width (in mm) | Height (in mm) |
|---|---|---|
| Image A | 60 | 40 |
| Image B | 40 | 20 |
| Image C | 30 | 20 |
| Image D | 90 | 60 |
| Image E | 60 | 60 |
Both factors are 3⁄2, so yes, they are the same.
Height: 40 × f = 60 ⇒ f = 60⁄40 = 3⁄2
In-text Questions — Page 1617.2 Ratios · 7.3 Ratios in their Simplest Form
By the factor 3⁄2, applied to both terms.
= 90 : 60
| Image | Width (in mm) | Height (in mm) |
|---|---|---|
| Image A | 60 | 40 |
| Image B | 40 | 20 |
| Image C | 30 | 20 |
| Image D | 90 | 60 |
| Image E | 60 | 60 |
Divide each pair of terms by their HCF.
Image E: 60 : 60, HCF = 60 → 60⁄60 : 60⁄60 = 1 : 1
Neither of these is 3 : 2, so the ratios of B and E are not proportional to those of A, C and D — which is the arithmetic behind what your eye already noticed.
In-text Questions — Pages 162–1637.4 Problem Solving with Proportional Reasoning (Examples 1–5)
Yes. Both have the same simplest form.
72 : 96, HCF = 24 → 72⁄24 : 96⁄24 = 3 : 4
So 3 : 4 :: 72 : 96
24.
96 = 2 × 2 × 2 × 2 × 2 × 3 = 2⁵ × 3
Common part = 2³ × 3 = 24
Dividing both terms of 72 : 96 by 24 gives 3 : 4.
30 spoons of sugar for the 18 extra glasses.
6 : 10 :: 18 : ?
First term: 6 → 18, factor = 18 ÷ 6 = 3
Second term must change by 3 as well: 10 × 3 = 30
6 : 10 :: 18 : 30
Divide the new term by the old term of the same quantity.
= 18 ÷ 6 = 3
No, Nitin is not correct. The two walls are equally strong.
Hari: length : bags = 40 : 2, HCF = 2 → 20 : 1
60 : 3 :: 40 : 2
This one needs your own school’s figures, but here is exactly how to settle it.
(one teacher for every 34 students)
Count the teachers and the students in your school, write the ratio, and reduce it. Then compare:
- If your simplest form is also 1 : 34, the two ratios are proportional.
- If it is 1 : 25, each teacher in your school handles fewer students.
- If it is 1 : 40, each teacher handles more.
Measure with a metre scale and reduce the ratio you get. A very common classroom size is 240 cm by 120 cm.
To draw a proportional rectangle in your notebook, pick any convenient factor and multiply both terms by it:
| Factor | Width | Height | Ratio |
| × 4 cm | 8 cm | 4 cm | 2 : 1 |
| × 5 cm | 10 cm | 5 cm | 2 : 1 |
| × 6.5 cm | 13 cm | 6.5 cm | 2 : 1 |
They will be of different sizes but the same shape — every one of them is a scaled copy of the blackboard.
In-text Questions — Pages 164–1657.4 Problem Solving with Proportional Reasoning (Examples 6–7) · Filter Coffee!
At age 3 the ratio is 1 : 10; at age 12 it is 4 : 13. No, it does not remain the same.
12 − 3 = 9 years later, mother is 30 + 9 = 39
12 : 39, HCF = 3 → 4 : 13
28 : 42, 6 : 9, 2 : 3.
___ : 42 → 42 ÷ 21 = 2, so first term = 14 × 2 = 28
6 : ___ → 6 ÷ 14 = 3⁄7, so second term = 21 × 3⁄7 = 9
2 : ___ → 14 ÷ 7 = 2, so second term = 21 ÷ 7 = 3
The factor is 3⁄7 — it must be a fraction, not an integer.
y = 6⁄14 = 3⁄7
Because it has more decoction for the same amount of milk: 20 : 30 = 2 : 3, against the regular 15 : 35 = 3 : 7.
Stronger: 20 mL decoction + 30 mL milk = 50 mL cup → decoction is 20⁄50 = 40%
Because a smaller share of the cup is decoction.
Ratio 10 : 40 = 1 : 4, against the regular 15 : 35 = 3 : 7
| Coffee Decoction (in mL) | Milk (in mL) | Regular/Strong/Light |
|---|---|---|
| 300 | 600 | |
| 150 | 500 | |
| 200 | 400 | |
| 24 | 56 | |
| 100 | 300 |
Reduce each row and compare it with the regular mix, 15 : 35 = 3 : 7.
| Coffee decoction (mL) | Milk (mL) | Simplest form | Decoction in the cup | Regular / Strong / Light |
| 300 | 600 | 1 : 2 | 300⁄900 = 33.3% | Strong |
| 150 | 500 | 3 : 10 | 150⁄650 = 23.1% | Light |
| 200 | 400 | 1 : 2 | 200⁄600 = 33.3% | Strong |
| 24 | 56 | 3 : 7 | 24⁄80 = 30% | Regular |
| 100 | 300 | 1 : 3 | 100⁄400 = 25% | Light |
Figure it Out — Pages 165–1677.4 Problem Solving with Proportional Reasoning
(i) 4 : 7 :: 12 : 21
(ii) 8 : 3 :: 24 : 6
(iii) 7 : 12 :: 12 : 7
(iv) 21 : 6 :: 35 : 10
(v) 12 : 18 :: 28 : 12
(vi) 24 : 8 :: 9 : 3
True: (i), (iv) and (vi).
| Statement | Cross multiply (ad and bc) | Simplest forms | True? |
| (i) 4 : 7 :: 12 : 21 | 4 × 21 = 84, 7 × 12 = 84 | 4 : 7 and 4 : 7 | True |
| (ii) 8 : 3 :: 24 : 6 | 8 × 6 = 48, 3 × 24 = 72 | 8 : 3 and 4 : 1 | False |
| (iii) 7 : 12 :: 12 : 7 | 7 × 7 = 49, 12 × 12 = 144 | 7 : 12 and 12 : 7 | False |
| (iv) 21 : 6 :: 35 : 10 | 21 × 10 = 210, 6 × 35 = 210 | 7 : 2 and 7 : 2 | True |
| (v) 12 : 18 :: 28 : 12 | 12 × 12 = 144, 18 × 28 = 504 | 2 : 3 and 7 : 3 | False |
| (vi) 24 : 8 :: 9 : 3 | 24 × 3 = 72, 8 × 9 = 72 | 3 : 1 and 3 : 1 | True |
8 : 18, 12 : 27, 16 : 36 — and there are infinitely many more.
4 : 9 × 3 → 12 : 27
4 : 9 × 4 → 16 : 36
First reduce: 18 : 24 = 3 : 4 (HCF = 6). Every answer must reduce to 3 : 4, so the second term is always 4⁄3 of the first.
12 : ___ → 12 × 4⁄3 = 16 → 12 : 16
20 : ___ → 20 × 4⁄3 = 80⁄3 = 26⅔ → 20 : 26⅔
27 : ___ → 27 × 4⁄3 = 36 → 27 : 36
A and D are similar to each other, and C and E are similar to each other. B is not similar to any of them.
Measure each rectangle’s two sides with your scale — three of them are printed at a slant, so measure along the sides, not across the page. Rounded to the nearest millimetre:
| Rectangle | Shorter side | Longer side | Longer : shorter | Nearest simple ratio |
| A | 6 mm | 18 mm | 3.0 | 3 : 1 |
| B | 12 mm | 18 mm | 1.5 | 3 : 2 |
| C | 20 mm | 51 mm | 2.55 | 5 : 2 |
| D | 13 mm | 39 mm | 3.0 | 3 : 1 |
| E | 7 mm | 17 mm | 2.43 | 5 : 2 |
The printed rectangle measures about 35 mm × 21 mm, so its width : height is 5 : 3. Multiply both terms by the same factor to get as many copies as you like.
| Factor | Width | Height | Ratio |
| × 0.4 cm (smaller) | 2 cm | 1.2 cm | 5 : 3 |
| the printed one | 3.5 cm | 2.1 cm | 5 : 3 |
| × 1.6 cm (bigger) | 8 cm | 4.8 cm | 5 : 3 |
No, your classmates’ rectangles will not all be the same size — and no, they are not wrong.
(a) 9 : 6 = 3 : 2 (b) 16 : 12 = 4 : 3
Wall (a) — one repeating block = 5 columns × 3 rows = 15 bricks.
Middle row: 2 coloured, 3 grey
Bottom row: 1 coloured, 4 grey
Coloured = 3 + 2 + 1 = 6, grey = 15 − 6 = 9
grey : coloured = 9 : 6 = 3 : 2
Wall (b) — one repeating block = 4 columns × 7 rows = 28 bricks.
Coloured = 1 + 2 + 2 + 2 + 2 + 2 + 1 = 12, grey = 28 − 12 = 16
grey : coloured = 16 : 12 = 4 : 3
Measure with a tape and record the lengths, then reduce each pair. Here is one real set of measurements from a student about 150 cm tall:
| Part | Length | Ratio asked for | Simplest form |
| head | 22 cm | head : torso = 22 : 55 | 2 : 5 |
| torso | 55 cm | torso : arms = 55 : 60 | 11 : 12 |
| arms | 60 cm | torso : legs = 55 : 80 | 11 : 16 |
| legs | 80 cm | — | — |
To draw the figure, choose one convenient factor and apply it to every measurement. Using 1⁄5 of the real lengths: head 4.4 cm, torso 11 cm, arms 12 cm, legs 16 cm.
Yes, the drawing looks far more realistic when the ratios are kept.
In-text Questions — Pages 167–170Trairasika — The Rule of Three (Examples 8–10) · Activity 1
10 kg of rice.
120 : 15 :: 80 : ?
Factor of change = 80⁄120 = 2⁄3
Rice = 15 × 2⁄3 = 10 kg
2⁄3 — the number of students has fallen to two-thirds of what it usually is.
A factor smaller than 1 means the quantity has decreased. The second term must be multiplied by the very same 2⁄3.
144 km.
150 : 90 :: 240 : x
Cross multiplying: 150 × x = 240 × 90
x = (240 × 90) ÷ 150
x = 21600 ÷ 150 = 144 km
No. The statement 150 : 90 :: 4 : ? mixes units — 150 is in minutes but 4 is in hours.
Right: 4 h = 240 min, so 150 : 90 :: 240 : ?
All three routes below give 144 km. Use whichever you find clearest.
- Unitary method. In 1 minute the car covers 90 ÷ 150 = 0.6 km. In 240 minutes it covers 240 × 0.6 = 144 km.
- Scaling the ratio. 240 ÷ 150 = 8⁄5, so multiply the distance by 8⁄5 as well: 90 × 8⁄5 = 144 km.
- Splitting the time. 150 min → 90 km, so 300 min → 180 km and 30 min → 18 km. Then 240 = 300 − 60, and 60 min → 36 km, giving 180 − 36 = 144 km.
No, they are not proportional. First put both weights in the same unit.
Meghalaya: 1 kg = 1000 g, so 1000 : 800 → HCF 200 → 5 : 4
1 : 1 is not 5 : 4, so the ratios are not proportional
The Himachal tea is more expensive — ₹1,000 per kg against ₹800 per kg.
Himachal: 200 g is 1⁄5 of a kg, so if 1 kg costs ₹x,
1⁄5 × x = 200
x = 200 × 5 = ₹1,000
Write the family recipe first, then scale every ingredient by one factor. Here is a worked example for upma cooked for a family of 5, with 15 guests invited so that 20 people must be fed.
| Ingredient | For 5 people | × 4 | For 20 people |
| Rava (semolina) | 250 g | 250 × 4 | 1000 g = 1 kg |
| Water | 600 mL | 600 × 4 | 2400 mL = 2.4 L |
| Onion | 1 medium | 1 × 4 | 4 medium |
| Oil | 2 tablespoons | 2 × 4 | 8 tablespoons |
| Salt | 1 teaspoon | 1 × 4 | 4 teaspoons |
Figure it Out — Pages 170–171Trairasika — The Rule of Three
About 1,80,76,923 km, that is roughly 1.81 crore kilometres in one week.
940 million km = 940 × 10⁶ = 94,00,00,000 km
52 : 940000000 :: 1 : x
x = 940000000 ÷ 52
x = 1,80,76,923 km (approximately)
15,660 bricks. First add up every foot of wall in the plan, then scale.
top edge 9 + 15 = 24 ft
bottom edge 9 + 15 = 24 ft
left side 12 ft, right side 12 ft
inner dividing wall 12 ft
Lower room (6 ft × 9 ft):
left 9 ft, right 9 ft, bottom 6 ft
Total = 24 + 24 + 12 + 12 + 12 + 9 + 9 + 6 = 108 ft
10 × x = 108 × 1450
x = 156600 ÷ 10 = 15,660 bricks
In-text Questions — Pages 171–172Trairasika — The Rule of Three · Activity 2
He will take less time — 1 hour 20 minutes. No, the problem cannot be written as 50 : 2 :: 75 : __, because when the speed increases, the time decreases.
At 75 km/h: time = 100 ÷ 75 = 4⁄3 hours
4⁄3 h = 1 h + 1⁄3 × 60 min = 1 hour 20 minutes
Collect real prices from a shop, then work out the price of one millilitre for each size — that single number makes all four containers comparable. For the sample table in the book:
| Container | Volume | Price | Price ÷ volume | Cost of 1 mL |
| Sachet | 6 mL | ₹2 | 2 ÷ 6 | ₹0.33 |
| Small Bottle | 180 mL | ₹154 | 154 ÷ 180 | ₹0.86 |
| Medium Bottle | 340 mL | ₹276 | 276 ÷ 340 | ₹0.81 |
| Large Bottle | 1000 mL | ₹540 | 540 ÷ 1000 | ₹0.54 |
The volume is not proportional to the price. If it were, every row of the last column would show the same figure; instead it runs 0.33, 0.86, 0.81, 0.54.
No.
Prices: 2 : 154, HCF = 2 → 1 : 77
1 : 30 is not 1 : 77
Cross multiplication says the same thing: 6 × 154 = 924 while 180 × 2 = 360.
The price of a container is not only the price of what is inside it.
Why not proportional: every pack has fixed costs (bottle, cap, label, filling, transport) that are spread over more shampoo in a big bottle; companies also give discounts on big packs and keep sachets cheap so that everyone can afford them.
| Small packs | Large packs | |
| For the customer | Low price today, easy to carry, no waste if used rarely | Usually cheaper per mL, fewer trips to the shop |
| For the company | Reaches more buyers, but far more packaging and handling per litre sold | Less packaging and handling per litre, larger sale at one go |
To reduce the ecological footprint: customers should buy the largest size they will actually use up and refill it; companies should sell refill packs and take back empty bottles.
Other products: yes, many packed goods cost less per unit in bigger packs; staples like rice or atta are usually priced closer to proportion.
In-text Questions — Pages 172–1757.5 Sharing, but Not Equally! · Activity 3 · Examples 11–12
6 : 6, which in its simplest form is 1 : 1.
6 : 6, HCF = 6 → 1 : 1
You get 7 counters, and the ratio of your partner’s counters to yours is 5 : 7.
partner : you = 5 : 7, and 5 and 7 have HCF 1, so it is already simplest
Your partner gets 9, you get 3.
Deal the counters out 3 and 1 at a time and see where it lands:
| Round | Partner takes | You take | Counters left |
| start | — | — | 12 |
| 1 | 3 | 1 | 8 |
| 2 | 3 | 1 | 4 |
| 3 | 3 | 1 | 0 |
| total | 9 | 3 | — |
Partner: 3 × 3 = 9 You: 1 × 3 = 3
Check: 9 : 3 = 3 : 1 ✓ and 9 + 3 = 12 ✓
Your partner gets 24, you get 18.
Size of each group = 42 ÷ 7 = 6
Partner: 4 × 6 = 24 You: 3 × 6 = 18
Check: 24 + 18 = 42 ✓ and 24 : 18 = 4 : 3 ✓
6 counters.
Size of each group = 42 ÷ 7 = 6
Every one of the seven groups holds 6 counters; four of them go to your partner and three to you.
Prashanti gets ₹3,000 and Bhuvan gets ₹1,000.
Total groups = 3 + 1 = 4
Each group = 4000 ÷ 4 = ₹1,000
Prashanti = 3 × 1000 = ₹3,000
Bhuvan = 1 × 1000 = ₹1,000
Check: 3000 + 1000 = 4000 ✓ and 3000 : 1000 = 3 : 1 ✓
2 kg of cement should be added.
Sand stays 30 kg. New ratio: 5 : 2 :: 30 : ?
Cement needed = 2⁄5 × 30 = 12 kg
Cement to add = 12 − 10 = 2 kg
Figure it Out — Page 1757.5 Sharing, but Not Equally!
₹1,800 and ₹2,700.
Each group = 4500 ÷ 5 = ₹900
First part = 2 × 900 = ₹1,800
Second part = 3 × 900 = ₹2,700
Check: 1800 + 2700 = 4500 ✓ and 1800 : 2700 = 2 : 3 ✓
40 mL of acid and 200 mL of water.
Each group = 240 ÷ 6 = 40 mL
Acid = 1 × 40 = 40 mL
Water = 5 × 40 = 200 mL
Check: 40 + 200 = 240 ✓ and 40 : 200 = 1 : 5 ✓
15 mL of blue and 25 mL of yellow. After adding the yellow, the new ratio is 1 : 3.
Each group = 40 ÷ 8 = 5 mL
Blue = 3 × 5 = 15 mL Yellow = 5 × 5 = 25 mL
Add 20 mL of yellow: yellow = 25 + 20 = 45 mL, blue is still 15 mL
blue : yellow = 15 : 45, HCF = 15 → 1 : 3
4 cups of rice and 2 cups of urad dal.
Each group = 6 ÷ 3 = 2 cups
Rice = 2 × 2 = 4 cups
Urad dal = 1 × 2 = 2 cups
Check: 4 + 2 = 6 ✓ and 4 : 2 = 2 : 1 ✓
3 : 13.
red = 3⁄8 bucket, yellow = 5⁄8 bucket
Add 1 whole bucket of yellow:
yellow = 5⁄8 + 1 = 13⁄8 bucket, red is unchanged at 3⁄8
red : yellow = 3⁄8 : 13⁄8
Multiply both terms by 8 → 3 : 13
Figure it Out — Pages 176–1777.6 Unit Conversions (chapter-end set)
2 : 3.
HCF of 600 and 900 = 300
600⁄300 : 900⁄300 = 2 : 3
4 buses are needed, and they will not all be full — 12 seats will be empty.
Buses needed = 204 ÷ 54 = 3.78, so 4 buses
Seats in 4 buses = 4 × 54 = 216
Empty seats = 216 − 204 = 12
Mumbai is more crowded — about 36,364 people in every square kilometre, against about 20,216 in Delhi.
Mumbai: 20 million ÷ 550 = 2,00,00,000 ÷ 550 ≈ 36,364 people per sq km
Your neck would be 4⁄10 = 2⁄5 of your height. Measure yourself and multiply.
Neck = 4⁄10 × your height = 0.4 × your height
For the crane: 4⁄10 × 155 = 62 cm of neck
If you are 150 cm tall: 4⁄10 × 150 = 60 cm
If you are 160 cm tall: 4⁄10 × 160 = 64 cm
52.5 palas of saffron.
3⁄7 : 5⁄2 :: 9 : x
Cross multiplying: 3⁄7 × x = 5⁄2 × 9
3⁄7 × x = 45⁄2
x = 45⁄2 × 7⁄3 = 315⁄6 = 52.5 palas
Harmain will be 4 years old (and her brother 8), that is, after 3 years.
Harmain: 1 + x, brother: 5 + x
(1 + x) : (5 + x) = 1 : 2
Cross multiplying: 2(1 + x) = 1(5 + x)
2 + 2x = 5 + x
x = 3
Harmain’s age = 1 + 3 = 4 years, brother = 5 + 3 = 8 ✓ and 4 : 8 = 1 : 2 ✓
18.5 kg.
37 : 2 :: x : 1
2 × x = 37 × 1
x = 37⁄2 = 18.5 kg
About 22.96 tonnes, that is roughly 22,957 kg of cow manure.
1 acre = 43,560 sq ft
Plot in acres = 100000 ÷ 43560 = 2.2957 acres
Manure = 10 × 2.2957 = 22.957 tonnes ≈ 22.96 tonnes
In kilograms: 22.957 × 1000 ≈ 22,957 kg
300 seconds, that is 5 minutes.
Number of mugfuls = 10000 ÷ 500 = 20
Time = 20 × 15 = 300 seconds = 5 minutes
About ₹82,645.
43560 : 1500000 :: 2400 : x
43560 × x = 2400 × 15,00,000
x = 3,60,00,00,000 ÷ 43560
x = ₹82,644.63 ≈ ₹82,645
Oxen: 120 hours. Tractor: 30 hours.
1 : 6 :: 20 : t ⇒ t = 20 × 6 = 120 hours
The tractor is 4 times faster, so it needs one-fourth of the time:
Per acre: 6 ÷ 4 = 1.5 hours
For 20 acres: 20 × 1.5 = 30 hours, or simply 120 ÷ 4 = 30 hours
Copper ≈ ₹5.26, nickel ≈ ₹2.59, together about ₹7.85.
Copper = 3 × 1.935 = 5.805 g
Nickel = 1 × 1.935 = 1.935 g
Copper: ₹906 per 1000 g → 5.805 × 906 ÷ 1000 = 5259.33 ÷ 1000 = ₹5.26
Nickel: ₹1341 per 1000 g → 1.935 × 1341 ÷ 1000 = 2594.835 ÷ 1000 = ₹2.59
Total metal cost ≈ ₹7.85
Puzzle Time — BinairoBinairo (Takuzu) — end of Part I
Here is the completed grid. Shaded cells are the ones printed in the book.
The completed grid:
The completed grid:
Chapter 7 of 13 – Maths
- Previous: Chapter 6 We Distribute Yet Things Multiply
- Next: Chapter 8 Fractions in Disguise
- All chapters: NCERT Solutions Class 8 Maths
Also for This Chapter
NCERT Solutions Class 8 Maths Chapter 7 Proportional Reasoning 1 – Overview
| Class | Class 8 |
| Subject | Maths |
| Chapter | 7 – Proportional Reasoning 1 |
| Textbook pages | 159 – 177 |
| Questions solved | 69 |
| Session | 2027 |
| Format | Full answers on this page + PDF |
NCERT Solutions Class 8 Maths Chapter 7 – FAQs
Where can I download NCERT Solutions Class 8 Maths Chapter 7 Proportional Reasoning 1 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 8 Maths book for 2027.
How many questions are solved in NCERT Class 8 Maths Chapter 7?
All 69 questions of the chapter (textbook pages 159 – 177) – 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.