Question:
A fraction has a numerator that is 4 less than its denominator. If 2 is added to both the numerator and the denominator, the resulting fraction becomes equal to 2/3. What was the original fraction?
एक भिन्न का अंश उसके हर से 4 कम है। यदि अंश और हर दोनों में 2 जोड़ दिया जाए, तो परिणामी भिन्न 2/3 के बराबर हो जाती है। मूल भिन्न क्या थी?
Options:
- 5/9
- 7/11
- 6/10
- 8/12
- 5/9
- 7/11
- 6/10
- 8/12
Correct Answer: c)
Explanation:
Let denominator be \(d\). Numerator is \(d – 4\).
Given: \(\dfrac{d – 4 + 2}{d + 2} = \dfrac{2}{3} \implies \dfrac{d – 2}{d + 2} = \dfrac{2}{3}\).
Cross-multiplying: \(3(d – 2) = 2(d + 2) \implies 3d – 6 = 2d + 4 \implies d = 10\).
Numerator = \(10 – 4 = 6\). Original fraction = 6/10.
माना हर = \(d\), तो अंश = \(d – 4\)।
प्रश्नानुसार: \(\dfrac{d – 2}{d + 2} = \dfrac{2}{3} \implies 3d – 6 = 2d + 4 \implies d = 10\)।
अंश = \(10 – 4 = 6\)। मूल भिन्न = 6/10 है।