Question

The ages of Hari and Harry are in ratio $ 5:7. $ Four years from now the ratio of their ages will be $ 3:4. $ Find their present ages.

Answer 1

Hint: Assign two variables to their present ages. Then form two linear equations using the two conditions given in the question. Then solve those linear equations to get the answer.

Complete step-by-step answer:
Let the present age of Hari be $ x. $
Let the present age of Harry be $ y. $
It is given to us that the present ages of Hari and Harry are in the ratio $ 5:7 $ . So we can write
 $ \dfrac{x}{y} = \dfrac{5}{7} $
 $ \Rightarrow x = \dfrac{5}{7}y $ . . . . . (1)
Now, four years later,
The age of Hari will be $ x + 4 $
And the age of Harry will be $ y + 4 $
Now, it is given to us that, the ages of Hari and Harry after four years are in the ratio $ 3:4 $
 $ \Rightarrow \dfrac{{x + 4}}{{y + 4}} = \dfrac{3}{4} $
 $ 4x + 16 = 3y + 12 $ . . . . . (2)
By substituting the value of $ x $ in equation (2) from equation (1), we get
 $ 4\left( {\dfrac{5}{7}y} \right) + 16 = 3y + 12 $
 $ \Rightarrow \dfrac{{20}}{7}y + 16 = 3y + 12 $
By simplifying it, we get
 $ \Rightarrow 3y - \dfrac{{20}}{7}y = 4 $
By cross multiplication, we get
 $ \Rightarrow \dfrac{{21y - 20y}}{7} = 4 $
Again, by cross multiplication and further simplification, we get
 $ y = 28 $
By substituting this value of $ y $ in equation (1), we get
 $ x = \dfrac{5}{7}y = \dfrac{5}{7} \times 28 = 20 $
 $ \therefore x = 20 $
Therefore, Hari’s present age is $ x = 20 $ years
And Harry’s present age is $ y = 28 $ years.

Note: You need to have a good understanding of the question to formulate the given information into mathematical equations. Read the question carefully. In this question, it was important to understand that the second ratio of ages was about four years later. So, you need to add four in the current ages before you take the ratio.