Question

The sum of present age of Madhav and Nidhi is 75 years. Madhav's age nine years from now will be twice of Nidhi's age twelve years ago. What's present age of Madhav

Answer 1

The present age of Madhav is 39 years.

• Let the present age of Madhav be x.

Let the present age of Nidhi be y.

• According to the first condition in the question,

x + y = 75  -(i)

• Madhav's age from 9 years now will be (x + 9)

Age of Nidhi 12 years ago was (y - 12)

• According to the second condition in the question,

x + 9 = 2 ( y - 12 )

Or, x + 9 = 2y - 24

Or, x - 2y = -24 - 9

Or, x - 2y = -33  -(ii)

• Multiplying equation (i) with 2, we get,

2x + 2y = 150 -(iii)

• Adding equation (ii) and (iii), we get,

x  -  2y  =  -33  -(ii)

2x +  2y  =  150 -(iii)

=> x  + 2x - 2y + 2y = -33 + 150

Or, 3x = 117

Or, x = 117 / 3

Or, x = 39

• Therefore, the present age of Madhav is 39 years.