Question:
The ratio between the daughter and father is 1:4. After 8 years, the ratio of their age becomes 2:5. What are the ages of the daughter and father?
पुत्री और पिता की आयु का अनुपात 1:4 है। 8 वर्ष बाद उनकी आयु का अनुपात 2:5 हो जाता है। पुत्री और पिता की वर्तमान आयु क्या है?
Options:
- 8, 32
- 10, 40
- 12, 48
- 14, 56
- 8, 32
- 10, 40
- 12, 48
- 14, 56
Correct Answer: a)
Explanation:
Let current ages be \(x\) and \(4x\).
After 8 years:
\(\dfrac{x + 8}{4x + 8} = \dfrac{2}{5}\)
\(5(x + 8) = 2(4x + 8) \implies 5x + 40 = 8x + 16\)
\(3x = 24 \implies x = 8\).
Father’s age = \(4 \times 8 = 32\).
Hence, their ages are 8 and 32 years.
माना वर्तमान आयु \(x\) और \(4x\) है।
\(\dfrac{x + 8}{4x + 8} = \dfrac{2}{5} \implies 5x + 40 = 8x + 16 \implies 3x = 24 \implies x = 8\)।
पिता की आयु = \(4 \times 8 = 32\)।
अतः वर्तमान आयु 8 और 32 वर्ष है।