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Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

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Present age of Jacob:

50

years and Jacob's son:

15

years

Present age of Jacob:

50

. years and Jacob's son:

10

years

Present age of Jacob:

40

years and Jacob's son:

10

years

Present age of Jacob:

35

years and Jacob's son:

15

years

answer is C.

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Detailed Solution

Given that, Jacob will be 3 times his son’s age five years later.
Let

x

be the present age of Jacob's son and

y

be the present age of Jacob.
Then as per the question

(y + 5) = 3 (x + 5) . . . . . . (1)

(y - 5) = 7 (x - 5) . . . . . . (2)

From equation

(1)

\Rightarrow y + 5 = 3 x + 15

\Rightarrow 3 x - y = - 10 . . . . . . (3)

From equation

(2)

\Rightarrow y - 5 = 7 x - 35

\Rightarrow 7 x - y = 30 . . . . . . . (4)

From equation

(3)

we get,

\Rightarrow - y = - 10 - 3 x

\Rightarrow y = 10 + 3 x

Substitute

y = 10 + 3 x

in equation

(4)

\Rightarrow 7 x - (10 + 3 x) = 30

\Rightarrow 7 x - 10 - 3 x = 30

\Rightarrow 4 x = 30 + 10

\Rightarrow 4 x = 40

\Rightarrow x = 10

Now, substituting

x = 10

in equation (1),

\Rightarrow 3 \times 10 - y = - 10

\Rightarrow 30 - y = - 10

\Rightarrow - y = - 40

\Rightarrow y = 40

Hence, Jacob's son's current age

= 10

years and Jacob's current age

= 40

years.
Therefore, option (3) is correct.

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Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their present ages?

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Detailed Solution

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