A is 20 years older than B. 5 years ago, A was 3 times as old as B. Find their present ages.

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35 years and 15 years

5 years and 25 years

18 years and 42 years

21 years and 44 years

answer is A.

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Detailed Solution

Given,
A is 20 years older than B.
Suppose
Current age of A = c
Current age of B = y Thus, by given condition,

x = y + 20 \dots (1)

Now, age of A 5 years ago= (x-5),
Age of A 5 years ago= (y-5)
Thus, again by the given condition,

(x - 5) = 3 (y - 5)

……(2)
Put the value of x from (1) into the equation (2),

(y + 20 - 5) = 3 (y - 5)

(y + 15) = 3 y - 15

\Rightarrow y = 15 years

Now put this value of y in equation (1) as,

x = y + 20

x = 15 + 20

x = 35 years

Thus, age of A = 35 years.
Age of B = 15 years.
Hence, option 1 is the correct answer.

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