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. Their present ages are.

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Jacob’s age = 30 years, Jacob’s son age = 10 years

Jacob’s age = 40 years, Jacob’s son age = 10 years

Jacob’s age = 50 years, Jacob’s son age = 15 years

Jacob’s age = 30 years, Jacob’s son age = 15 years

answer is B.

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Detailed Solution

Given the age of Jacob will be three times that of his son after five years. Also, Jacob's age was seven times that of his son before 5 years.
Age of Jacob = x
Age of Jacob’s son = y
According to the question,

x + 5 = 3 (y + 5)

x + 5 = 3 y + 15

x - 3y = 10 ---- 1
Also,
x – 5 = 7(y - 5)
x – 5 = 7y - 35
x - 7y = - 30 ----- 2
From equation 1,
- 3y = 10 - x

y = − (10 − x) 3

Now, value of x is,
Putting in equation 2,

x − 7 y = − 30

x − 7 − 10 + x 3 = − 30

3 x + 70 − 7 x = − 30 × 3

3 x − 7 x = − 90 − 70

− 4 x = − 160

x = 40
Now, the value of y is,

x − 3 y = 10

40 − 3 y = 10

3 y = 40 − 10

3 y = 30

y = 10
Present age of Jacob is 40 years and age of his son is 10 years.
Hence, option 2 is correct.

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