Question

The sum of present age of manish and gautam is 65. After 15 years, the ratio of their ages will be 9 : 10. Find the difference between their present ages.

Answer 1

Difference between their present ages is 5 years.

Step-by-step explanation:

Let the present age of Manish be $x$ years.

     and present age of Gautam be $y$ years.

• First condition says that the sum of present age of Manish and Gautam is 65, i.e.;

                           $x+y = 65$

                           $x = 65 - y$ ---------- [Equation 1]

• Second condition says that after 15 years, the ratio of their ages will be 9 : 10, i.e.;

                           $\frac{x+15}{y+15} = \frac{9}{10}$

                         $10(x+15) = 9(y+15)$

                         $10(65-y+15) = 9(y+15)$   {using equation 1}

                         $10(80-y) = 9(y+15)$

                         $800-10y = 9y + 135$

                         $10y+9y = 800-135$

                            $19y = 665$

                              $y=\frac{665}{19}$ = 35

Putting value of  $y$ in equation 1, we get;

                     $x = 65-35$ = 30

Therefore, Present age of Manish = $x$ = 30 years

                  Present age of Gautam = $y$ = 35 years

So, difference between their present ages = 35 - 30 = 5 years.