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A father’s age is now three times that of his elder daughter. 5 years back, his age was 8 times that of his younger daughter. If the difference of ages of the two daughters is 5 years, what is the age of the father now?
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- 55
- 50
- 60
- 45
Correct Option: D
Suppose the present age of younger daughter is P years.
Given : - Present age of the elder daughter - the present age of younger daughter = 5
∴ Present age of the elder daughter = P + 5 years
Present age of the father = 3 × Present age of the elder daughter
Present age of the father = 3(P + 5) years.
According to the question,
5 years before, 8 × ( the present age of younger daughter - 5 years ) = Present age of the father - 5 years
⇒ 8 (P – 5) = (3P + 15) – 5
⇒ 8P – 40 = 3P + 10
⇒ 8P – 3P = 10 + 40
| ∴ P = | = 10 years | 5 |
Present age of father = 3(P + 5) = 3 × 10 + 15 = 45 years { ∴ putting , P = 10 }
