Question

The ages of Sahil and Nikhil are in the ratio 4 :3 five years hence, the ratio of their ages will be 5:4 find their present ages

Answer 1

Present age of Sahil is 20 years

Present age of Nikhil is 15 years.

Step-by-step explanation:

We are given that the ages of Sahil and Nikhil are in the ratio 4 : 3 and five years hence, the ratio of their ages will be 5 : 4.

Let the present age of Sahil be x years

and the present age of Nikhil be y years.

• First condition states that the ages of Sahil and Nikhil are in the ratio    4 : 3, that means;

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

                          $x=\frac{4y}{3}$  ------------------ [Equation 1]

• Second condition states that five years hence, the ratio of their ages will be 5 : 4, that means;

                            $\frac{x+5}{y+5} =\frac{5}{4}$

                           $4(x+5)=5(y+5)$

                           $4x+20=5y+25$

                            $4\times \frac{4y}{3} +20=5y+25$         {using equation 1}

                            $\frac{16y}{3} +20=5y+25$

Now, we will try to make the denominator on left hand side of expression and then cross multiplying;

                             $\frac{16y+60}{3} =5y+25$

                             ${16y+60} =3(5y+25)$

                             ${16y+60} =15y+75$

                             ${16y-15y=75-60$

                                    y = 15 years

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

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

                                $x =\frac{4\times 15}{3}$ = 20 years.

Therefore, Present age of Sahil is x = 20 years and Present age of Nikhil is y = 15 years.