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A and B can together complete a task in 20 hours. after 5 hours A Ieaves. B takes 45 hours to finish the remaining task. How many hours would A have taken to complete the entire task. if he worked alone from the beginning?

1. 30 hours
2. 40 hours
3. 48 hours
4. 60 hours

A और B एक साथ किसी कार्य को 20 घंटे में पूरा करते हैं। 5 घंटे पश्चात A कार्य छोड़ देता है। शेष कार्य को पूर्ण करने में B को 45 घंटे लगते हैं। यदि A अकेले पूरे कार्य को आरम्भ से करता तो उसे कार्य पूर्ण करने में कितने घंटे लगे होते?

1. 30 घंटे
2. 40 घंटे
3. 48 घंटे
4. 60 घंटे

This Question came in

UGC-NET-Hindi-17-June-2023-Shift-2-Q21

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Detailed Explanation & Answer

Fraction of work done A and B together in 5 hours = 5/20 = 1/4
After 5 hours A leaves,
Remaining work = 1-1/4 = 3/4

Since B take 45 hours to done remaining 3/4th of work
=> time is taken by B alone to complete the work alone = 45x4/3 = 60 hours.
now,
time taken by A to complete the work if done alone = 1/(1/20 - 1/60) = 60/2 = 30 hours.

5 घंटे में A और B द्वारा मिलकर किये गये कार्य का अंश = 5/20 = 1/4
5 घंटे बाद A चला जाता है,
शेष कार्य = 1-1/4 = 3/4

चूँकि B को शेष 3/4 काम पूरा करने में 45 घंटे लगते हैं
=> B द्वारा अकेले कार्य पूरा करने में लिया गया समय = 45x4/3 = 60 घंटे।
अब,
A द्वारा अकेले कार्य पूरा करने में लिया गया समय = 1/(1/20 - 1/60) = 60/2 = 30 घंटे।

The Correct Answer is 1

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