Question

the present age of Rajni and Ragini are in the ratio 7:9. five years from now the ratio of their ages will be 4:5. find their present age.

please explain it by step by step​

Answer 1

Given :

• Present Age of Rajni and Ragini are in ratio 7:9.
• After 5 years their ages will be in ratio 4:5.

To Find :

• Present Age of Ragni and Ragini.

Solution :

$\longmapsto\tt{Let\:Present\:Age\:of\:Rajni\:be=7x}$

$\longmapsto\tt{Let\:Present\:Age\:of\:Ragini\:be=9x}$

After 5 years :

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

$\longmapsto\tt{Age\:of\:Ragini=9x+5}$

A.T.Q :

$\longmapsto\tt{\dfrac{7x+5}{9x+5}=\dfrac{4}{5}}$

$\longmapsto\tt{5(7x+5)=4(9x+5)}$

$\longmapsto\tt{35x+25=36x+20}$

$\longmapsto\tt{35x-36x=20-25}$

$\longmapsto\tt{-1x=-5}$

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

Value of x is 5...

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Rajni=7(5)}$

$\longmapsto\tt\bold{35\:yrs.}$

$\longmapsto\tt{Present\:Age\:of\:Ragini=9(5)}$

$\longmapsto\tt\bold{45\:yrs.}$