Question

10 years ago, the ages of A and B were in the ratio of 13:17.17 years from now the ratio of their age will be 10:11 what is the age of B at present?

Answer 1

Answer:I don't know

Step-by-step explanation:

Answer 2

Present age of B is 27 years .

Step-by-step explanation:

Let the present age of A be $x$ years

and present age of B be $y$ years.

• First condition states that 10 years ago, the ages of A and B were in the ratio of 13 : 17, i.e.;

                       $\frac{x-10}{y-10} = \frac{13}{17}$

                      $17(x-10) = 13(y-10)$

                      $17x - 170 = 13y - 130$

                      $17x = 13y + 40$

                        $x = \frac{13y+40}{17}$  ---------- [Equation 1]

• Second condition states that 17 years from now the ratio of their age will be 10 : 11, i.e.;

                         $\frac{x+17}{y+17} = \frac{10}{11}$

                      $11(x+17) = 10(y+17)$

                      $11x + 187= 10y +170$

                      $11x = 10y - 17$

                      $x = \frac{10y - 17}{11}$

Now putting value of $x$ from equation 1 into above equation, we get;

                     $\frac{13y+40}{17} = \frac{10y - 17}{11}$

                    11($13y$ + 40) = 17($10y$ - 17)

                     $143y$ + 440 = $170y$ - 289

                     $170y-143y$ = 440 + 289

                              $27y$ = 729

                                $y = \frac{729}{27}$ = 27

Therefore, present age of B is 27 years.