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Is it true that if the sum of the ages of a father and his son in years is $65$ and twice the difference of their ages in years is $50$ , then the age of the father is $45$ years?

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True

False

answer is A.

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Detailed Solution

It is given if the sum of the ages of a father and his son in years is

65

and twice the difference of their ages in years is

50

, then the age of the father is

45

years.
Let,
Father's age

= x

Son's age

= y

As per question,

x + y = 65

\Rightarrow y = 65 - x

.....(1)
Therefore,

2 (x - y) = 50

\Rightarrow 2 x - 2 y = 50

.......(2)
Substituting value of

y

from equation (1) in equation (2),

\Rightarrow 2 x - 2 (65 - x) = 50

\Rightarrow 2 x - 130 + 2 x = 50

\Rightarrow x = 45

So father's age

= 45

years.
Therefore, if the sum of the ages of a father and his son in years is

65

and twice the difference of their ages in years is

50

, then the age of the father is

45

years is true.
Hence, correct option is 1.

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