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UGC-NET-Paper1

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A man invested 1/3 of his retirement gratuity at 6% simple interest; 1/4 of his gratuity at 7% and the rest at 8% simple interest. If his annual return on these investments is Rs 7012.5. find the total amount of gratuity invested by the man.

1. Rs 89,000
2. Rs 99.000
3. Rs 95,000
4. Rs 1,05,000

किसी व्यक्तिने अपनी सेवा-निवृत्ति उपदान का 1/3 भाग 6% साधारण ब्याज की दर से; उपदान का 1/4 भाग 7% और शेष को 8% साधारण ब्याज की दर से निवेश किया । यदि इन निवेशों पर उसकी वार्षिक प्राप्ति रुपये 7012.5 है, तो व्यक्ति द्वारा निवेश की गई कुल उपदान की धनराशि ज्ञात कीजिए |

1. 89,000 रुपये
2. 99,000 रुपये
3. 95,000 रुपये
4. 1,05,000 रुपये
This Question came in
UGC-NET-English-01-March-2023-Shift-1-Q23
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Detailed Explanation & Answer
Let's denote retirement gratuity = a rs.

SI of 1/3 of a at 6% = a x 1/3 x 6/100 = a / 50
SI of 1/4 of a at 7% = a x 1/4 x 7/100 = 7a / 400

Remaining amount = a - a/3 - a/4 = 5a/12
SI of 5a/12 at 8% = a / 30

Total Interest = a/50 + 7a/400 + a/30 = (24a + 21a + 40a) / 1200
85a / 1200 = 7012.5
a = 7012.5 x 1200 / 85 = 99000
आइए निरूपित करें सेवानिवृत्ति ग्रेच्युटी = एक रु.

6% पर 1/3 का एसआई = ए एक्स 1/3 x 6/100 = ए / 50
7% पर 1/4 का एसआई = ए x 1/4 x 7/100 = 7ए/400

शेष राशि = a - a/3 - a/4 = 5a/12
8% पर 5ए/12 का एसआई = ए/30

कुल ब्याज = a/50 + 7a/400 + a/30 = (24a + 21a + 40a) / 1200
85ए/1200 = 7012.5
ए = 7012.5 x 1200/85 = 99000
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