# Math Problems : Simultaneous Equations

## Question

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?

- 30
- 40
- 20
- 16
- 28

#### Correct Answer

Choice (2). 40

#### Explanatory Answers

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.

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