Question 53

The ratio of the ages of two boys is 3:4. After 3 years, the ratio will be 4:5.The ratio of their ages after 21 years will be

Solution

Let the present ages of the two boys respectively be $$3x$$ and $$4x$$ years

Ratio after 3 years

=> $$\frac{3x+3}{4x+3}=\frac{4}{5}$$

=> $$15x+15=16x+12$$

=> $$16x-15x=15-12$$

=> $$x=3$$

$$\therefore$$ Ratio of ages after 21 years = $$\frac{3x+21}{4x+21}$$

= $$\frac{3(3)+21}{4(3)+21}=\frac{9+21}{12+21}$$

= $$\frac{30}{33}=\frac{10}{11}$$

=> Ans - (D)

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