The ratio between the ages of $A$ and $B$ is $2 : 5$ . After $8$ years, their ages will be in the ratio $1 : 2$ . What is the difference between their present ages?

20

years

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22

years

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24

years

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25

years

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Solution

The correct option is C $24$ years
Let $A = 2 x; B = 5 x$ be the present ages of $A$ and $B$ respectively.
After $8$ years, their ages will be $(2 x + 8)$ years and $(5 x + 8)$ years respectively.
Therefore, $(2 x + 8) : (5 x + 8) :: 1 : 2$
$\Rightarrow (5 x + 8) \times 1 = 2 (2 x + 8)$
$\Rightarrow x = 8$
Thus difference of their present ages is $5 x - 2 x = 3 x$ i.e., $24$ years.

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The ratio between the ages of A and B is 2:5. After 8 years, their ages will be in the ratio 1:2. What is the difference between their present ages?

The correct option is C 24 yearsLet A=2x;B=5x be the present ages of A and B respectively.After 8 years, their ages will be (2x+8) years and (5x+8) years respectively.Therefore, (2x+8):(5x+8)::1:2⇒(5x+8)×1=2(2x+8)⇒x=8Thus difference of their present ages is 5x−2x=3x i.e., 24 years.

The ratio between the ages of $A$ and $B$ is $2 : 5$ . After $8$ years, their ages will be in the ratio $1 : 2$ . What is the difference between their present ages?