Question

2 years before Anu’s age is 10 less than double the age of Manu. After 4years Anu’s age is 6 more than the age of Manu. What is the age of Anu and Manu now ?

Answer 1

S O L U T I O N :

Let the present age of Anu's be x years & let the present age of Manu's be y years respectively.

A/q

$\underbrace{\bf{2\:years\:ago\::}}$

The age of Anu's was = (x - 2) years.

The age of Manu's was = (y - 2) years.

So,

$\mapsto\tt{(x-2) = 2(y-2)-10}$

$\mapsto\tt{x-2= 2y-4-10}$

$\mapsto\tt{x-2= 2y-14}$

$\mapsto\tt{x-2y=-14+2}$

$\mapsto\tt{x-2y=-12................(1)}$

$\underbrace{\bf{4\:years\:later\::}}$

The age of Anu's will = (x + 4) years.

The age of Anu's will = (y + 4) years.

So,

$\mapsto\tt{(x+4) = (y+4)+6}$

$\mapsto\tt{x+4 = y+10}$

$\mapsto\tt{x- y=10-4}$

$\mapsto\tt{x- y=6}$

$\mapsto\tt{x=6+y................(2)}$

∴ Putting the value of x in equation (1),we get;

$\mapsto\tt{(6+y)-2y=-12}$

$\mapsto\tt{6+y-2y=-12}$

$\mapsto\tt{6-y=-12}$

$\mapsto\tt{-y=-12-6}$

$\mapsto\tt{\cancel{-}y=\cancel{-}18}$

$\mapsto\bf{y=18\:years}$

∴ Putting the value of y in equation (2),we get;

$\mapsto\tt{x=6+18}$

$\mapsto\bf{x=24\:years}$

Thus,

The present age of Anu's age will be [24 years] & the present age of Manu's age will be [18 years] .