Question

The ages of Ajay and Bhaskar are in the ratio 5:7 .Five years from now, the ratio of their ages will be 5:6. Find their present ages.
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Answer 1

$\huge{ \purple{ANSWER:}}$

${ \red{Given : }}$

The ratio of ajay and bhaskar present ages is 5:7

${ \blue{Solution: }}$

So, let there ages be 5x and 7x

After 5 years there ratio will be 5:6

Therefore,

$\frac{(5x + 5) }{(7x + 5)} = \frac{5}{6}$

$6(5x + 5) = 5(7x + 5)$

$(30x + 30) = (35x + 25)$

$30 - 25 = 35x - 30x$

$5 = 5x$

$x = \frac{5}{5}$

$x = 1$

Therefore,

The present age of ajay is 5x = 5×1 = 5 years

The present age of bhaskar is 7x =7×1 = 7 years

Answer 2

Given :

The ages of Ajay and Bhaskar are in the ratio 5:7 .

Five years from now, the ratio of their ages will be 5:6 .

To Find :

Present Age of Ajay and Bhaskar .

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:Ajay\:be=5x}$

$\longmapsto\tt{Let\:Present\:age\:of\:Bhaskar\:be=7x}$

After 5 years :

$\longmapsto\tt{Age\:of\:Ajay=5x+5}$

$\longmapsto\tt{Age\:of\:Bhaskar=7x+5}$

A.T.Q :

$\longmapsto\tt{\dfrac{5x+5}{7x+5}=\dfrac{5}{6}}$

$\longmapsto\tt{6(5x+5)=5(7x+5)}$

$\longmapsto\tt{30x+30=35x+25}$

$\longmapsto\tt{30x-35x=25-30}$

$\longmapsto\tt{-5x=-5}$

$\longmapsto\tt{x=\cancel\dfrac{-5}{-5}}$

$\purple\longmapsto\:\large\underline{\boxed{\bf\blue{x}\pink{=}\red{1}}}$

Value of x is 1 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Ajay=5(1)}$

$\longmapsto\tt\bf{5\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:Bhaskar=7(1)}$

$\longmapsto\tt\bf{7\:yrs}$