Question

The ages of Tom and Sally are in the ratio 5:7. 4 years ago ratio of their age was two ratio three. find their present age
3 points
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Answer 1

The present age of Tom is 20 years

The present age of Sally is 28 years.

Step-by-step explanation:

We are given that the ages of Tom and Sally are in the ratio 5 : 7.

Also, 4 years ago ratio of their age was two ratio three.

Let the present age of Tom be x years and the present age of Sally be y years.

• First condition says that the ages of Tom and Sally are in the ratio 5:7, that is;

                                     $\frac{x}{y} = \frac{5}{7}$

                                     $x=\frac{5y}{7}$  ----------------- [Equation 1]

• Second condition says that 4 years ago ratio of their age was 2 : 3, that is;

                                    $\frac{x-4}{y-4} = \frac{2}{3}$

                         $3\times ({x-4} )= {2}\times ({y-4})$

                               $3x-12=2y-8$      

                                  $3x=2y+4$ 

                            $3 \times \frac{5y}{7}=2y+4$         {using equation 1}

                                 $\frac{15y}{7}=2y+4$      

                                 ${15y}{}=14y+28$

                                 $15y-14y=28$

                                   y = 28 years

Now, putting the value of y in equation 1, we get;

                                    $x=\frac{5y}{7}$

                                    $x=\frac{5\times 28}{7}$ = 20 years

Therefore, the present age of Tom is x = 20 years and the present age of Sally is y = 28 years.

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