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Q.

5 years ago, a man was 7 times as old as his son. After 5 years he will be thrice as old as his son. Find their present ages and choose the option which follows.

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a

Age of son=5 years; Age of man=40 years.

b

Age of son=10 years; Age of man=80 years

c

Age of son=6 years; Age of man=48 years

d

None of these

answer is A.

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Detailed Solution

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It is given that 5 years ago, a man was 7 times as old as his son and after 5 years he will be thrice as old as his son.
Assume the age of the son 5 years back be x.
Then according to the condition, the man’s age is 7 times his son’s age.
So, we can express the present ages of the man and the son as follows,
Son’s present age

= x + 5

Man’s present age

= 7 x + 5

Now, as per the condition, five years later, the man will be thrice as old as his son.
Using this, we can set up an equation as follows,

\begin{matrix} 7 x + 5 + 5 = 3 (x + 5 + 5) \\ 7 x + 10 = 3 (x + 10) \\ 7 x + 10 = 3 x + 30 \end{matrix}

7 x + 10 - 10 = 3 x + 30 - 10

7 x = 3 x + 20

\begin{matrix} 7 x - 3 x = 3 x + 20 - 3 x \\ 4 x = 20 \end{matrix}

\begin{matrix} \frac{4 x}{4} = \frac{20}{4} \\ x = 5 \end{matrix}

So, the son’s present age is 5+5=10 years.
Similarly, present age of the father is

(7 \times 5) + 5 = 35 + 5 = 40 years

.
The present age of the son is 10 years and the age of the father is 40 years.
Hence, the correct option is (1).

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