The ages of Hari and Harry are in the ratio 5: 7 . Four years from now the ratio of their ages will be 3: 4. Find their present ages.

Given:

The ratio of ages of Hari and Harry is  5: 7

Four years from now the ratio of their ages will be 3: 4.

To do:  Find their present age.

Solution:

Let's take their present ages at $5 x$   and  $7 x$

Four years from now the ratio of their ages will be  3: 4

Four years from now their ages will be  $5 x + 4$   and   $7 x + 4$

so ,  $5 x + 4  :  7 x + 4  =  3 : 4$

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

Cross multiply

$4 (5 x + 4)  =  3 (7 x + 4)$

$20 x + 16  =  21 x + 12$

$16  -  12   =  21 x  -  20 x$[keep variables on one side, and numbers on the other side]

$4   =   x$

rewrite,

$x  =  4$

So, present ages are $5 x$  and  $7 x$

Now, substitute $x = 4$  in present ages,

5 (4)  :  7 (4)  =  20  :  28

So, the present ages of Hari and Harry are  20  and  28 which is ratio 3:4.

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Updated on: 10-Oct-2022

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