Question 140

The ratio of the ages of A and B seven years ago was 3 : 4 respectively. The ratio of their ages nine years from now will be 7 : 8 respectively. What is B’s age at present?

Solution

Let present age of A = $$x$$ years and present age of B = $$y$$ years

Seven years ago,

=> $$\frac{x - 7}{y - 7} = \frac{3}{4}$$

=> $$4x - 28 = 3y - 21$$

=> $$4x - 3y = 7$$ -------------Eqn(1)

After 9 years,

=> $$\frac{x + 9}{y + 9} = \frac{7}{8}$$

=> $$8x + 72 = 7y + 63$$

=> $$8x - 7y = -9$$ --------------Eqn(2)

Solving equations (1) and (2), we get :

$$y = 23$$

$$\therefore$$ Present age of B = 23 years

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