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A father says to his son, “7 years ago my age was 7 times of your age at that time and after 3 years my age will be thrice of your age.” The present age of the son is:
- A15 years
- B12 years
- C21 years
- D24 years
Answer not set
Discussion 1
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CCommunity
Let, son’s present age = x
And father’s present age = y
7 years ago,
Son’s age = x - 7
Father’s age = y - 7
But according to the condition given,
Father’s age 7 yrs ago = 7 × son’s age 7 yrs ago
y - 7 = 7 × (x - 7) → y - 7 = 7x - 49 → 7x - y = 42 ----(1)
3 years later,
son’s age = x + 3
Father’s age = y + 3
But according to given condition,
Father’s age after 7 yrs = 7 × son’s age after 7 yrs
y + 3 = 3 × (x + 3) → y + 3 = 3x + 9 → 3x - y = - 6 ----(2)
Solving (1) & (2),
From eqn. (1), y = 7x - 42
Hence, 3x - 7x + 42 = - 6
42 - 4x = - 6 → 4x = 48 → x = 12
Therefore y = (7 × 12) - 42 = 42
And father’s present age = y
7 years ago,
Son’s age = x - 7
Father’s age = y - 7
But according to the condition given,
Father’s age 7 yrs ago = 7 × son’s age 7 yrs ago
y - 7 = 7 × (x - 7) → y - 7 = 7x - 49 → 7x - y = 42 ----(1)
3 years later,
son’s age = x + 3
Father’s age = y + 3
But according to given condition,
Father’s age after 7 yrs = 7 × son’s age after 7 yrs
y + 3 = 3 × (x + 3) → y + 3 = 3x + 9 → 3x - y = - 6 ----(2)
Solving (1) & (2),
From eqn. (1), y = 7x - 42
Hence, 3x - 7x + 42 = - 6
42 - 4x = - 6 → 4x = 48 → x = 12
Therefore y = (7 × 12) - 42 = 42