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UGC-NET-Paper1

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Suppose there is a fraction whose numerator and denominator are both positive integers. If the numerator is increased by 20% and the denominator is decreased by 20% then its value becomes 6/9. What is that fraction?

1. 1/9
2. 2/9
3. 1/3
4. 4/9

मान लीजिए कि कोई भिन्‍न है जिसका अंश तथा हर दोनो धनात्मक पूर्णाक हैं। यदि अंश में 20% की वृद्धि हो जाए और हर में 20% की कमी की जाए तो उसका मान 6/9 हो जाता है। वह भिन्‍न क्या है?

1. 1/9
2. 2/9
3. 1/3
4. 4/9

This Question came in

UGC-NET-Hindi-08-January-2025-Shift-1-Q32

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Detailed Explanation & Answer

Let the original fraction be x/y.

Numerator increased by 20% → becomes 1.2x
Denominator decreased by 20% → becomes 0.8y

New fraction = 1.2x / 0.8y = 6 / 9

Now simplify:
1.2x / 0.8y = 6 / 9
3x / 2y = 6 / 9
3x * 9 = 2y * 6
27x = 12y
Divide both sides by 3:
9x = 4y
So, x/y = 4/9

The original fraction is 4/9

Answer is 4

मान लीजिए कि मूल भिन्न x/y है।

अंश में 20% की वृद्धि → 1.2x हो जाता है

हर में 20% की कमी → 0.8y हो जाता है

नई भिन्न = 1.2x / 0.8y = 6 / 9

अब सरल करें:
1.2x / 0.8y = 6 / 9
3x / 2y = 6 / 9
3x * 9 = 2y * 6
27x = 12y
दोनों पक्षों को 3 से विभाजित करें:
9x = 4y
तो, x/y = 4/9

मूल भिन्न 4/9 है

उत्तर 4 है

The Correct Answer is 4

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