Question

The present ages of A and B in the ratio 7:5 . ten years later, their ages will be in the ratio 9:5 . Find their present ages.​

Answer 1

Correct Question -

The present ages of A and B in the ratio 7:5 . ten years later, their ages will be in the ratio 9:7 . Find their present ages.

Solution -

In the above questión , it is mentioned that the ages of A and B are in the ratio 7 : 5 .

Ten years later , their ages will be in the ratio of 9 : 7 .

We have to find their present ages.

So let us proceed .

It is quite obvious that A is older than B

Let the present ages of A and B be 7x and 5x respectively.

After 10 years ;

Age of A > 7x + 10

Age of B > 5x + 10

This is in a ratio of 9 : 7

> [ 7x + 10]/[ 5x + 10] = 9/7

> 45x + 90 = 49x + 70

> 4x = 20

> x = 5

Present Age of A > 7x = 35

Present Age of B > 5x = 25

The present ages of A and B are 35 and 25 respectively . This is the required answer .

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Answer 2

Given :-

The  present ages of A and B in the ratio 7:5 . ten years later, their ages will be in the ratio 9:5

To Find :-

Present ages

Solution :-

Let the present ages be 7x and 5x

$\sf \dfrac{7x+10}{5x+10} = \dfrac{9}{7}$

$\sf 7(7x + 10) = 9(5x + 10)$

$\sf 49x + 70=45x + 90$

$\sf 49x - 45x = 90 - 50$

$\sf 4x=20$

$\sf x = \dfrac{20}{4}$

$\sf x =5$

Present age of A = 7(5) = 35 years

Present age of B = 5(5) = 25 years