Question

The age of Anu and Anju are in ratio 5:7.Four year later their age's will be in ratio 3:4. find their present age

Answer 1

Given :-

• Present age ratio of Anu and Anju is 5 : 7

• After 4 years ratio will be 3 : 4

To Find :-

• Present age of Anu and Anju .

Solution :-

Let's assume that present age of Anu = 5x and Anju is 7x .

After 4 years their age wil be

Anu's age = 5x + 4

Anju's age = 7x +4 .

So ratio will be -

$\sf{ \frac{Anu}{Anju} = \frac{5x + 4}{7x + 4} }$

But according to the question

$\sf{\frac{Anu}{Anju} = \frac{3}{4} }$

Equating both ratios :-

$\sf{\implies \frac{5x +4 }{7x + 4} = \frac{3}{4} }$

$\sf{\implies 4[5x +4 ] = 3 [7x +4] }$

$\sf{\implies 20x + 16 = 21x + 12}$

$\sf{\implies 16 - 12 = 21x - 20x }$

$\boxed{\sf{\implies x = 4}}$

So putting the value of x where we assumed age of both girls

$\underline{\rm{Anu;s \; age \; = 5[4] \rightarrow 20 \; years }}$

$\underline{\rm{Anju;s \; age \; = 7[4] \rightarrow 28 \; years }}$

Verification -

$\sf{\frac{20}{28} = \frac{4 \times 5}{7 \times 4} \rightarrow \frac{5}{7}}$

Hence verified