TANCET Quant : Linear Equations, Word Problems

Here is a word problem that requires you to frame a pair of linear equations, solve the equations to arrive at an answer.

Rajesh is 10 years younger to Baskar. 10 years back, Rajesh's age was two-thirds that of Baskar's. How old is Baskar now?
1. 30
2. 40
3. 20
4. 16
5. 28

Correct Answer is Choice (2). 40 years.

Explanatory Answer

Let the present age of Baskar be 'b' and that of Rajesh be 'r'.
So, r = b - 10 .... eqn (1).

10 years back Rajesh was (r - 10) years old. 10 years back Baskar was (b - 10) years old.
The question states that 10 years back Rajesh was two thirds as old as Baskar was.

i.e., (r - 10) = (2/3)*(b - 10) .... eqn (2).
Cross multiplying, we get 3(r - 10) = 2(b - 10)
or 3r - 30 = 2b - 20 .... eqn (2)

From eqn (1) we can substitute r as (b - 10) in eqn (2)
So, 3(b - 10) - 30 = 2b - 20
or 3b - 30 - 30 = 2b - 20
or b = 40.

The present age of Baskar is 40 years.