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Q.

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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a

Present age of Jacob:50years and Jacob's son: 15years

b

Present age of Jacob:50. years and Jacob's son: 10years

c

Present age of Jacob:40years and Jacob's son: 10years

d

Present age of Jacob:35years and Jacob's son: 15years  

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),
 ⇒y+5=3x+15
⇒3x-y=-10......(3)
From equation (2),
⇒y-5=7x-35
⇒7x-y=30 .......(4)
From equation (3) we get,
⇒-y=-10-3x
⇒y=10+3x
Substitute y=10+3x in equation 4,
⇒7x-(10+3x)=30
⇒7x-10-3x=30
⇒4x=30+10
⇒4x=40
⇒x=10
Now, substituting x=10 in equation (1),
⇒3×10-y=-10
⇒30-y=-10
⇒-y=-40
⇒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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