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UGC-NET-Paper1

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Read the Question carefully and choose the correct option.
Ayush and Bilal can do a job in ‘D’ days. If Ayush can alone do the job in D+3 days and Bilal alone can do the job in D+12 days, find the value of D.

1. 9
2. 8
3. 6
4. 5

आयुष और बिलाल एक काम को ‘D’ दिनों में पूरा कर सकते हैं। यदि आयुष अकेले उस काम को D+3 दिनों में पूरा कर सकता है और बिलाल अकेले उस काम को D+12 दिनों में पूरा कर सकता है, तो D का मान ज्ञात कीजिए।

1. 9
2. 8
3. 6
4. 5
This Question came in
UGC-NET-LibSci-16-January-2025-Shift-2-Q30
UGC-NET Paper 1 Full Course

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Detailed Explanation & Answer
### Given:
Ayush alone in D+3 days → Work rate = 1/(D+3)
Bilal alone in D+12 days → Work rate = 1/(D+12)
Together in D days → Work rate = 1/D

### Equation:
1/(D+3) + 1/(D+12) = 1/D

### Solve:
Take LCM:
(D+12 + D+3) / [(D+3)(D+12)] = 1/D
(2D+15) / [(D+3)(D+12)] = 1/D

Cross multiply:
(2D+15)D = (D+3)(D+12)
2D² + 15D = D² + 15D + 36
D² = 36
D = 6

### Answer:
**(3) 6**
### दिया गया:
आयुष अकेले D+3 दिन → कार्य दर = 1/(D+3)
बिलाल अकेले D+12 दिन → कार्य दर = 1/(D+12)
साथ में D दिन → कार्य दर = 1/D

### समीकरण:
1/(D+3) + 1/(D+12) = 1/D

### हल करें:
LCM लें:
(D+12 + D+3) / [(D+3)(D+12)] = 1/D
(2D+15) / [(D+3)(D+12)] = 1/D

क्रॉस गुणा करें:
(2D+15)D = (D+3)(D+12)
2D² + 15D = D² + 15D + 36
D² = 36
D = 6

### उत्तर:
**(3) 6**
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