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Father's age is three times the sum of ages of his two children. After 5 years, his age will be twice the sum of ages of two children. Find the age of father.

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45 years

40 years

44 years

43 years

answer is A.

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Detailed Solution

It is given that father's age is three times the sum of ages of his two children.
Let Father’s age

= x years

and sum of ages of his two children

= y years

.
Since, the father's age is three times the sum of ages of his two children then,

x = 3 y

… (1)
After five years,
Father’s age

= (x + 5) years

And
Sum of ages of his two children

= (y + 10) years

Since, after 5 years, father’s age will be twice the sum of ages of two children then,

x + 5 = 2 (y + 10)

\Rightarrow x + 5 = 2 y + 20

\Rightarrow x - 2 y = 15

Putting

x = 3 y

from equation (1) in above,

3 y - 2 y = 15 \Rightarrow y = 15

Putting

y = 15

in equation (1),

x = 3 y = 3 \times 15 = 45

Therefore,
Father’s age

= 45 years

Hence, option (1) is correct.

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