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.

Answer 1

Answer:

present age of Ajay is 5 years old

and present age of Bhaskar is 7 years old

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 :

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

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

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

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