In NTSE, about 5 questions are based on word problems at least. The main thing to keep in mind while handling such questions is to not get carried away by the statements, but to extract data efficiently. To help you better, we will narrow down on some most frequently asked types.
- Age related problems
- Distance and Speed related problems
- Unitary Method
- Ratio and Proportion
- Simple Equations
Age Problems
Eg : Four years ago Ram was four times as old as Shyam. Today he is twice as old. How old is Ram now?
Now remember, try to keep least variables. Let us take a variable x.
x = Shyam’s age 4 years ago
4*x = Ram’s age 4 years ago
x+4 = Shyam’s age now
4*x+4 = Ram’s age now
After you have decided your variables, now write the equations.
Ram’s age today =2 times Shyam’s age today
4x + 4 = 2x + 8
Subtract 2x from each side:
2x + 4 = 8
Subtract 4 from each side:
2x = 4
Divide both sides by 2:
x=2
Now note, this is only “x”. The question asked requires you to find Ram’s age now which is 4*x+4 = 12! Voila!
So in Age problems, you just need to take a variable, identify ages at different stages, then equate as per relation given.
Distance and Speed Relations
These should not be messed up. Just remember the thumb rule equations
Distance = speed x time
Speed = distance / time
Time = distance / speed
Also, take care of units. For example, if time is given in minutes, and speed is in Km/hr, convert all units to least denomination. Or as per your convenience. For example in case of minutes and Km/hr you can convert speed to m/sec and time to seconds or only convert speed to Km/minutes ( though you might get confused).
Unitary Method
Eg: The average salary of 20 workers in an office is Rs. 1900 per month. If manager’s salary is added the average salary becomes Rs. 2000 per month. What is the manager’s annual salary? (NTSE MAT 2009)
It is simply required to identify – what is information for x number of items and from that derive information for y number of items. From x, derive information for 1 item and from that, do for y.
For example the above question can be solved like this
Let manager’s salary be “x”
Total salary of workers = 20×1900=38000
Total salary of workers and manager=38000+x
New average salary=(38000+x)/21 [because new total number of people is 20+1]
New average salary=2000
So we can equate
(38000+x)/21=2000
Multiplying by 21 on both sides
38000+x=42000
Subtracting 38000 from both sides
x=4000
Thus the salary of the manager is 4000!
Ratio and Proportion
Solving these problems can be done simply by writing the ratios in terms of fractions and carrying operation of multiplication and division or simply cross multiplying.
Eg- 2:x=3:9
Write this as fraction – (2/x)= (3/9)
Cross multiplying
2*9=3*x
(2*9)/3=x
6=x
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