Question

The sum of the present ages of a person and his daughter is 42 years. Six years hence the ratio of their ages will be 7: 2. Find the difference between their present ages

Answer 1

Difference between their present ages is 30 years.

Step-by-step explanation:

Let the present age of a person be $x$ years.

     and present age of his daughter be $y$ years.

• First condition says that the sum of present age of a person and his daughter is 42 years, i.e.;

                           $x+y = 42$

                           $x = 42 - y$ ---------- [Equation 1]

• Second condition says that Six years hence the ratio of their ages will be 7 : 2, i.e.;

                           $\frac{x+6}{y+6} = \frac{7}{2}$

                         $2(x+6) = 7(y+6)$

                         $2(42-y+6) = 7(y+6)$   {using equation 1}

                         $2(48-y) = 7(y+6)$

                         $96-2y = 7y+42$

                         $7y+2y = 96-42$

                            $9y = 54$

                              $y=\frac{54}{9}$ = 6

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

                     $x = 42-6$ = 36

Therefore, Present age of a person = $x$ = 36 years

                  Present age of his daughter = $y$ = 6 years

So, difference between their present ages = 36 - 6 = 30 years.