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A couple got married when both of them were 20 years old. After ‘x’ years a son was born and ‘y’ years later they had twin daughters. Presently the total age of the family is 116 years and the youngest member is 10 years old. If the ratio of the age of the mother and the son is 5 : 2, what is the present age (in years) of the son?
  • a)
    12
  • b)
    15
  • c)
    18
  • d)
    16
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A couple got married when both of them were 20 years old. After &lsquo...
Couple got married at the age of 20, x years later a boy was born, y years later two girls were born and each girl is aged 10 years presently
Age of boy = y + 10
Age of the couple = 20 + x + y + 10 = 30 + x + y
(30 + x + y) : (y + 10) = 5 : 2
10 + 2x = 3y -------------- (1)
2(30 + x + y) + y + 10 + 2 × 10 = 116
2x + 3y = 26 --------------- (2)
Solving equations (1) and (2) we get:
x = 4 and y = 6
Present age of the boy = y + 10 = 16 years
Hence, option D is correct.
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Community Answer
A couple got married when both of them were 20 years old. After &lsquo...
Given information:

- Couple got married at the age of 20
- 'x' years later, a son was born
- 'y' years later, they had twin daughters
- Total family age is 116 years
- Youngest member is 10 years old
- Ratio of mother's age to son's age is 5:2

Calculations:

Let the present age of the son be S years.
- Mother's age = 5S (as per the given ratio)
- Son's age = S years

Calculation of other family members' ages:
- Father's age = 20 + S (as he was 20 when the son was born)
- Twin daughters' age = 20 + S + x + y (as they were born 'x' and 'y' years after the son)

Total family age:
- Total family age = Mother's age + Father's age + Son's age + 2 * (Twin daughters' age) + 10 (for the youngest member)
116 = 5S + 20 + S + S + 2 * (20 + S + x + y) + 10
116 = 7S + 70 + 40 + 2x + 2y + 10
116 = 7S + 120 + 2x + 2y

Solving for S:
7S = 116 - 120 - 2x - 2y
7S = -4 - 2x - 2y
S = (-4 - 2x - 2y) / 7

Given that the youngest member is 10 years old:
S = 10
-4 - 2x - 2y = 70
2x + 2y = -74
x + y = -37 (which is not possible as they cannot have negative ages)

Therefore, the assumption that the son is 10 years old is incorrect.
The correct present age of the son can be calculated using the correct values of 'x' and 'y'.
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A couple got married when both of them were 20 years old. After ‘x’ years a son was born and ‘y’ years later they had twin daughters. Presently the total age of the family is 116 years and the youngest member is 10 years old. If the ratio of the age of the mother and the son is 5 : 2, what is the present age (in years) of the son?a)12b)15c)18d)16Correct answer is option 'D'. Can you explain this answer?
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