Question 60

Four years ago, the ratio of the ages of A and B was 2 : 1. Four years hence, this ratio will become 3 : 2. What is the ratio of their present ages?

Solution

Let their ages 4 years ago be a,b respectively.

4 years ago,
$$\frac{a }{ b} = \frac{2}{1}$$

$$a=2b$$ ......(1)

4 years hence, means a+8,b+8
$$\frac{a+8}{b+8} = \frac{3 }{ 2}$$
by cross multiplying.
$$2a + 16 = 3b +24$$ ......(2)

solving above two equations for a and b, we get
a= 16
b= 8

so their present ages are
a+4 = 20
b+4 = 12

$$\frac{a }{ b} = \frac{20}{12}$$

$$\frac{a }{ b} = \frac{5}{3}$$

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