Time and Work – 50 Questions with Answers

Time and Work – 50 Questions with Answers (समय और कार्य – 50 प्रश्न उत्तर सहित)

1. A can complete a work in 12 days. How much work will he do in 4 days? (एक व्यक्ति 12 दिनों में कार्य पूरा करता है। वह 4 दिनों में कितना कार्य करेगा?)

Answer: Work done in 4 days = (4/12) = 1/3 of the work.

उत्तर: 4 दिनों में किया गया कार्य = (4/12) = कार्य का 1/3 भाग।

2. A and B can do a work in 20 and 30 days respectively. How long will they take to complete the work together? (A और B क्रमशः 20 और 30 दिनों में कार्य पूरा करते हैं। वे मिलकर कार्य कितने दिनों में पूरा करेंगे?)

Answer: Work/day by A = 1/20, by B = 1/30; Together = 1/20 + 1/30 = (3+2)/60 = 5/60 = 1/12; Time taken = 12 days.

उत्तर: A का दैनिक कार्य = 1/20, B का = 1/30; मिलकर = 1/20 + 1/30 = (3+2)/60 = 5/60 = 1/12; समय = 12 दिन।

3. A does 60% of a work in 9 days. In how many days will he complete the whole work? (A 9 दिनों में कार्य का 60% करता है। वह पूरा कार्य कितने दिनों में करेगा?)

Answer: Work/day = 60%/9 = 20% per day; So, time = 100% / 20% = 5 days.

उत्तर: दैनिक कार्य = 60%/9 = 20% प्रति दिन; तो समय = 100% / 20% = 5 दिन।

4. A can do a work in 15 days and B in 10 days. If A starts the work and after 5 days B joins him, how long will it take to complete the work? (A 15 दिनों में और B 10 दिनों में कार्य पूरा करते हैं। A 5 दिन काम करता है फिर B जुड़ता है, तो कार्य पूरा होने में कितना समय लगेगा?)

Answer: Work done by A in 5 days = 5/15 = 1/3; Remaining work = 2/3; Work/day together = 1/15 + 1/10 = (2+3)/30 = 5/30 = 1/6; Time to finish = (2/3) ÷ (1/6) = 4 days; Total time = 5 + 4 = 9 days.

उत्तर: A द्वारा 5 दिन में किया गया कार्य = 5/15 = 1/3; शेष कार्य = 2/3; साथ में दैनिक कार्य = 1/15 + 1/10 = (2+3)/30 = 5/30 = 1/6; शेष कार्य पूरा करने में समय = (2/3) ÷ (1/6) = 4 दिन; कुल समय = 5 + 4 = 9 दिन।

5. A and B can do a work in 24 and 16 days respectively. If they work alternately, starting with A, how long will it take to complete the work? (A और B क्रमशः 24 और 16 दिनों में कार्य पूरा करते हैं। यदि वे वैकल्पिक दिन काम करते हैं और A पहले शुरू करता है, तो कार्य पूरा होने में कितना समय लगेगा?)

Answer: Work/day by A = 1/24, B = 1/16. In two days, work done = 1/24 + 1/16 = (2/48 + 3/48) = 5/48. Days needed for full work = 48/5 × 2 = 19.2 days (approximately 20 days).

उत्तर: A का दैनिक कार्य = 1/24, B का = 1/16. दो दिनों में कार्य = 1/24 + 1/16 = (2/48 + 3/48) = 5/48. पूर्ण कार्य के लिए दिन = 48/5 × 2 = 19.2 दिन (लगभग 20 दिन)।

6. A can do a work in 18 days, B in 24 days, and C in 36 days. They all work together. How long will they take to finish the work? (A 18 दिनों, B 24 दिनों और C 36 दिनों में कार्य पूरा करते हैं। वे मिलकर काम करते हैं। कार्य पूरा करने में कितना समय लगेगा?)

Answer: Work/day = 1/18 + 1/24 + 1/36 = (4/72 + 3/72 + 2/72) = 9/72 = 1/8; Time = 8 days.

उत्तर: दैनिक कार्य = 1/18 + 1/24 + 1/36 = (4/72 + 3/72 + 2/72) = 9/72 = 1/8; समय = 8 दिन।

7. A is twice as efficient as B. If B can do a work in 12 days, how long will A take to do the work? (A, B से दुगना कुशल है। यदि B 12 दिनों में कार्य करता है, तो A कितने दिनों में करेगा?)

Answer: Since A is twice efficient, A will take 12/2 = 6 days.

उत्तर: चूंकि A दुगना कुशल है, A का समय = 12/2 = 6 दिन।

8. A can do a work in 15 days and B is 50% more efficient than A. How long will B take to do the work? (A 15 दिनों में कार्य करता है और B, A से 50% अधिक कुशल है। B कितने दिनों में कार्य करेगा?)

Answer: B’s efficiency = 1.5 × A; So, time taken by B = 15 / 1.5 = 10 days.

उत्तर: B की दक्षता = 1.5 × A; इसलिए B का समय = 15 / 1.5 = 10 दिन।

9. A and B together can do a work in 10 days. B alone can do it in 15 days. How long will A alone take to do the work? (A और B मिलकर 10 दिनों में कार्य करते हैं। B अकेला 15 दिनों में करता है। A अकेला कितने दिनों में करेगा?)

Answer: Work/day A+B = 1/10, B = 1/15; So, A = 1/10 – 1/15 = (3-2)/30 = 1/30; Time taken by A = 30 days.

उत्तर: A+B का दैनिक कार्य = 1/10, B = 1/15; इसलिए A = 1/10 – 1/15 = (3-2)/30 = 1/30; A का समय = 30 दिन।

10. Two pipes can fill a tank in 20 and 30 minutes respectively. If both are opened together, how long will it take to fill the tank? (दो पाइप क्रमशः 20 और 30 मिनट में टंकी भरते हैं। दोनों साथ खोलने पर कितना समय लगेगा?)

Answer: Filling rate = 1/20 + 1/30 = (3+2)/60 = 5/60 = 1/12; Time to fill = 12 minutes.

उत्तर: भरने की दर = 1/20 + 1/30 = (3+2)/60 = 5/60 = 1/12; भरने का समय = 12 मिनट।

11. A can do a work in 10 days, B in 15 days, and C in 20 days. They work together for 2 days. What fraction of the work is left? (A 10 दिनों, B 15 दिनों और C 20 दिनों में कार्य करते हैं। वे 2 दिन मिलकर काम करते हैं। कितना कार्य बचा?)

Answer: Work/day = 1/10 + 1/15 + 1/20 = (6+4+3)/60 = 13/60; Work done in 2 days = 2 × 13/60 = 26/60 = 13/30; Remaining = 1 – 13/30 = 17/30.

उत्तर: दैनिक कार्य = 1/10 + 1/15 + 1/20 = (6+4+3)/60 = 13/60; 2 दिन में कार्य = 2 × 13/60 = 26/60 = 13/30; बचा कार्य = 1 – 13/30 = 17/30।

12. A, B, and C can do a work in 8, 12, and 24 days respectively. B and C start working and A joins after 3 days. How long will the whole work take? (A, B, C क्रमशः 8, 12 और 24 दिनों में कार्य करते हैं। B और C काम शुरू करते हैं और A 3 दिन बाद जुड़ता है। पूरा कार्य कितना समय लगेगा?)

Answer: Work/day B+C = 1/12 + 1/24 = (2+1)/24 = 3/24 = 1/8; Work done in 3 days = 3 × 1/8 = 3/8; Remaining work = 5/8; Work/day A+B+C = 1/8 + 1/12 + 1/24 = (3+2+1)/24 = 6/24 = 1/4; Time to finish = (5/8) ÷ (1/4) = 2.5 days; Total = 3 + 2.5 = 5.5 days.

उत्तर: दैनिक कार्य B+C = 1/12 + 1/24 = (2+1)/24 = 3/24 = 1/8; 3 दिन में कार्य = 3 × 1/8 = 3/8; बचा कार्य = 5/8; दैनिक कार्य A+B+C = 1/8 + 1/12 + 1/24 = (3+2+1)/24 = 6/24 = 1/4; पूरा करने का समय = (5/8) ÷ (1/4) = 2.5 दिन; कुल = 3 + 2.5 = 5.5 दिन।

13. A takes twice as much time as B to do a work. If both work together, they can do it in 12 days. How long will B alone take? (A, B से दुगना समय लेता है। वे साथ में 12 दिनों में काम पूरा करते हैं। B अकेला कितना समय लेगा?)

Answer: Let B’s time = x days, A’s time = 2x; Work/day A+B = 1/x + 1/2x = 3/2x; 3/2x = 1/12 → x = 18 days.

उत्तर: मान लें B का समय = x दिन, A = 2x; दैनिक कार्य A+B = 1/x + 1/2x = 3/2x; 3/2x = 1/12 → x = 18 दिन।

14. A is thrice as efficient as B. Working together, they can complete the work in 8 days. How long will B take to do it alone? (A, B से तीन गुना कुशल है। वे मिलकर 8 दिनों में कार्य करते हैं। B अकेला कितना समय लेगा?)

Answer: Let B’s time = x days; A’s time = x/3; Work/day A+B = 1/x + 3/x = 4/x = 1/8; So, x = 32 days.

उत्तर: मान लें B का समय = x दिन; A का समय = x/3; दैनिक कार्य A+B = 1/x + 3/x = 4/x = 1/8; इसलिए x = 32 दिन।

15. Two people can do a work in 9 days. One of them is twice as efficient as the other. Find the time taken by each to do the work alone. (दो लोग 9 दिनों में काम करते हैं। एक की दक्षता दूसरे से दुगनी है। प्रत्येक अकेले कितना समय लेंगे?)

Answer: Let slower person’s time = x days; faster person = x/2; Together work/day = 1/x + 2/x = 3/x = 1/9; So, x = 27 days; Faster person = 27/2 = 13.5 days.

उत्तर: मान लें धीमे व्यक्ति का समय = x दिन; तेज़ व्यक्ति = x/2; मिलकर कार्य/दिन = 1/x + 2/x = 3/x = 1/9; तो x = 27 दिन; तेज़ व्यक्ति = 27/2 = 13.5 दिन।

16. A can do a work in 20 days. B is 25% more efficient than A. How long will B take to do the work? (A 20 दिनों में काम करता है। B, A से 25% अधिक कुशल है। B कितना समय लेगा?)

Answer: B’s time = 20 / 1.25 = 16 days.

उत्तर: B का समय = 20 / 1.25 = 16 दिन।

17. A can do a work in 12 days. After working 4 days, he is joined by B who can do the work in 16 days. Find how long it takes to complete the work. (A 12 दिनों में काम करता है। 4 दिन बाद B जुड़ता है जो 16 दिनों में करता है। पूरा काम कब होगा?)

Answer: Work done by A in 4 days = 4/12 = 1/3; Remaining work = 2/3; Work/day A+B = 1/12 + 1/16 = (4+3)/48 = 7/48; Time to finish = (2/3) ÷ (7/48) = (2/3) × (48/7) = 32/7 ≈ 4.57 days; Total time = 4 + 4.57 = 8.57 days.

उत्तर: A द्वारा 4 दिन में किया गया कार्य = 4/12 = 1/3; बचा कार्य = 2/3; A+B का दैनिक कार्य = 1/12 + 1/16 = (4+3)/48 = 7/48; पूरा करने का समय = (2/3) ÷ (7/48) = (2/3) × (48/7) = 32/7 ≈ 4.57 दिन; कुल समय = 4 + 4.57 = 8.57 दिन।

18. A can do a work in 15 days. B and C together can do the same work in 10 days. If A, B, and C work together, they complete the work in 6 days. Find how long B and C take to do the work together. (A 15 दिनों में काम करता है। B और C मिलकर 10 दिनों में करते हैं। A, B, C साथ में 6 दिनों में करते हैं। B और C अकेले कितना समय लेंगे?)

Answer: Work/day A = 1/15; A+B+C = 1/6; So B+C = 1/6 – 1/15 = (5-2)/30 = 3/30 = 1/10; So B and C together take 10 days.

उत्तर: A का दैनिक कार्य = 1/15; A+B+C = 1/6; तो B+C = 1/6 – 1/15 = (5-2)/30 = 3/30 = 1/10; B और C साथ में 10 दिन लेंगे।

19. A can do a work in 18 days. B works twice as fast as A but works only half the time A works. Who will finish the work first? (A 18 दिनों में काम करता है। B A से दोगुना तेज़ है लेकिन आधा समय काम करता है। कौन पहले काम पूरा करेगा?)

Answer: A’s rate = 1/18; B’s rate = 2 × 1/18 = 1/9 but B works half the time, so effective work/day = (1/9) × (1/2) = 1/18; Both finish at the same time.

उत्तर: A की दर = 1/18; B की दर = 2 × 1/18 = 1/9 लेकिन आधा समय काम करता है, प्रभावी कार्य/दिन = (1/9) × (1/2) = 1/18; दोनों एक ही समय में पूरा करेंगे।

20. Two pipes fill a tank in 24 and 36 minutes respectively. Both pipes are opened together but the second pipe is closed after 12 minutes. How long will it take to fill the tank? (दो पाइप 24 और 36 मिनट में टंकी भरते हैं। दोनों साथ खोलते हैं लेकिन दूसरे पाइप को 12 मिनट बाद बंद कर दिया जाता है। पूरा भरने में कितना समय लगेगा?)

Answer: Work done in first 12 minutes = 12(1/24 + 1/36) = 12(3/72 + 2/72) = 12(5/72) = 5/6; Remaining = 1 – 5/6 = 1/6; Filled by first pipe alone = 1/24 per minute; Time = (1/6) ÷ (1/24) = 4 minutes; Total time = 12 + 4 = 16 minutes.

उत्तर: पहले 12 मिनट में कार्य = 12(1/24 + 1/36) = 12(3/72 + 2/72) = 12(5/72) = 5/6; बचा = 1 – 5/6 = 1/6; पहले पाइप की दर = 1/24 प्रति मिनट; समय = (1/6) ÷ (1/24) = 4 मिनट; कुल समय = 12 + 4 = 16 मिनट।

21. A can do a piece of work in 24 days and B can do it in 18 days. They work on it together for 6 days. What fraction of work is left? (A 24 दिनों में काम करता है और B 18 दिनों में। वे 6 दिन मिलकर काम करते हैं। कितना काम बचा?)

Answer: Work/day A+B = 1/24 + 1/18 = (3+4)/72 = 7/72; Work done in 6 days = 6 × 7/72 = 7/12; Remaining = 1 – 7/12 = 5/12.

उत्तर: दैनिक कार्य A+B = 1/24 + 1/18 = (3+4)/72 = 7/72; 6 दिन में किया गया कार्य = 6 × 7/72 = 7/12; बचा कार्य = 1 – 7/12 = 5/12।

22. A can do a work in 30 days. B is twice as efficient as A. How many days will B take to finish the work? (A 30 दिनों में काम करता है। B, A से दो गुना कुशल है। B कितना दिन लेगा?)

Answer: B’s time = 30 / 2 = 15 days.

उत्तर: B का समय = 30 / 2 = 15 दिन।

23. Two people can do a work in 12 days. If one takes 4 days more than the other, find the time taken by each. (दो लोग 12 दिनों में काम करते हैं। एक दूसरे से 4 दिन अधिक लेता है। दोनों का समय ज्ञात करें।)

Answer: Let time taken by first = x days, second = x + 4 days; Work/day together = 1/x + 1/(x+4) = 1/12;
Solve: (2x+4)/(x(x+4)) = 1/12 → 24x + 48 = x² + 4x → x² – 20x – 48 = 0;
Solve quadratic → x = 24 (approx), other = 28 days.

उत्तर: मान लें पहला व्यक्ति = x दिन, दूसरा = x + 4 दिन; मिलकर कार्य/दिन = 1/x + 1/(x+4) = 1/12;
हल करें: (2x+4)/(x(x+4)) = 1/12 → 24x + 48 = x² + 4x → x² – 20x – 48 = 0;
हल करने पर x ≈ 24 दिन, दूसरा = 28 दिन।

24. A and B can do a work in 16 and 24 days respectively. They work alternately one day each, starting with A. In how many days will the work be finished? (A और B क्रमशः 16 और 24 दिनों में काम करते हैं। वे बारी-बारी से एक दिन काम करते हैं, A से शुरू करते हुए। काम कब पूरा होगा?)

Answer: Work/day A = 1/16, B = 1/24;
Work in 2 days (A+B) = 1/16 + 1/24 = (3+2)/48 = 5/48;
Work in 14 days = 7 cycles = 7 × 5/48 = 35/48;
Remaining = 13/48, next day A works = 1/16 = 3/48, Remaining = 10/48;
Next day B works = 1/24 = 2/48, Remaining = 8/48;
Next day A works again = 1/16 = 3/48, Remaining = 5/48;
Next day B works = 1/24 = 2/48, Remaining = 3/48;
Next day A works = 1/16 = 3/48, work finished;
Total days = 14 + 5 = 19 days.

उत्तर: A का दैनिक कार्य = 1/16, B = 1/24;
2 दिन में कार्य (A+B) = 1/16 + 1/24 = (3+2)/48 = 5/48;
14 दिन में कार्य = 7 चक्र = 7 × 5/48 = 35/48;
बचा = 13/48, अगले दिन A काम करता है = 1/16 = 3/48, बचा = 10/48;
अगले दिन B काम करता है = 1/24 = 2/48, बचा = 8/48;
फिर A = 3/48, बचा = 5/48;
फिर B = 2/48, बचा = 3/48;
फिर A = 3/48, पूरा हुआ;
कुल दिन = 14 + 5 = 19 दिन।

25. A alone can do a work in 10 days. B alone can do it in 15 days. C alone in 20 days. They all work together for 3 days. How much work is left? (A अकेले 10 दिन, B 15 दिन, C 20 दिन में काम करते हैं। वे 3 दिन मिलकर काम करते हैं। कितना काम बचा?)

Answer: Work/day A+B+C = 1/10 + 1/15 + 1/20 = (6+4+3)/60 = 13/60;
Work done in 3 days = 3 × 13/60 = 39/60 = 13/20;
Remaining = 1 – 13/20 = 7/20.

उत्तर: दैनिक कार्य A+B+C = 1/10 + 1/15 + 1/20 = (6+4+3)/60 = 13/60;
3 दिन में किया गया कार्य = 3 × 13/60 = 39/60 = 13/20;
बचा कार्य = 1 – 13/20 = 7/20।

26. A can do a work in 14 days, B in 21 days. They start working together, but B leaves after 6 days. How long will A take to finish the remaining work? (A 14 दिन, B 21 दिन में काम करता है। वे साथ काम शुरू करते हैं, B 6 दिन बाद छोड़ देता है। A बचा काम कब पूरा करेगा?)

Answer: Work done in 6 days by A+B = 6 × (1/14 + 1/21) = 6 × (3/42 + 2/42) = 6 × 5/42 = 30/42 = 5/7;
Remaining = 1 – 5/7 = 2/7;
A alone rate = 1/14;
Time by A = (2/7) ÷ (1/14) = 4 days;
Total time = 6 + 4 = 10 days.

उत्तर: 6 दिन में A+B द्वारा कार्य = 6 × (1/14 + 1/21) = 6 × (3/42 + 2/42) = 6 × 5/42 = 30/42 = 5/7;
बचा कार्य = 1 – 5/7 = 2/7;
A की दर = 1/14;
A का समय = (2/7) ÷ (1/14) = 4 दिन;
कुल समय = 6 + 4 = 10 दिन।

27. A and B together can do a work in 9 days. B and C together can do the same work in 12 days. A and C together can do it in 18 days. Find the time taken by A, B, and C individually. (A और B 9 दिन, B और C 12 दिन, A और C 18 दिन में काम करते हैं। A, B, C अकेले कितना समय लेंगे?)

Answer: Let A’s rate = a, B’s rate = b, C’s rate = c;
a + b = 1/9, b + c = 1/12, a + c = 1/18;
Adding all: 2(a + b + c) = 1/9 + 1/12 + 1/18 = (4/36 + 3/36 + 2/36) = 9/36 = 1/4;
So a + b + c = 1/8;
Subtract a + b from total: c = 1/8 – 1/9 = (9-8)/72 = 1/72 → C takes 72 days;
Similarly, A = 1/8 – 1/12 = (3-2)/24 = 1/24 → A takes 24 days;
B = 1/8 – 1/18 = (9-4)/72 = 5/72 → B takes 72/5 = 14.4 days.

उत्तर: मान लें A की दर = a, B = b, C = c;
a + b = 1/9, b + c = 1/12, a + c = 1/18;
सब जोड़ें: 2(a + b + c) = 1/9 + 1/12 + 1/18 = (4/36 + 3/36 + 2/36) = 9/36 = 1/4;
तो a + b + c = 1/8;
a + b घटाएं: c = 1/8 – 1/9 = (9-8)/72 = 1/72 → C = 72 दिन;
इसी तरह, A = 1/8 – 1/12 = (3-2)/24 = 1/24 → A = 24 दिन;
B = 1/8 – 1/18 = (9-4)/72 = 5/72 → B = 72/5 = 14.4 दिन।

28. Two pipes can fill a tank in 20 and 30 minutes respectively. Both pipes are opened together, but the second pipe is closed after 10 minutes. How long will it take to fill the tank? (दो पाइप 20 और 30 मिनट में टंकी भरते हैं। दोनों साथ खोले जाते हैं लेकिन दूसरे को 10 मिनट बाद बंद कर दिया जाता है। टंकी भरने में कितना समय लगेगा?)

Answer: Work done in 10 mins = 10(1/20 + 1/30) = 10(3/60 + 2/60) = 10 × 5/60 = 5/6;
Remaining = 1 – 5/6 = 1/6;
First pipe fills at 1/20 per min;
Time to fill remaining = (1/6) ÷ (1/20) = 20/6 = 3⅓ mins;
Total time = 10 + 3⅓ = 13⅓ minutes.

उत्तर: 10 मिनट में कार्य = 10(1/20 + 1/30) = 10(3/60 + 2/60) = 10 × 5/60 = 5/6;
बचा = 1 – 5/6 = 1/6;
पहला पाइप 1/20 प्रति मिनट भरता है;
बचा भरने का समय = (1/6) ÷ (1/20) = 20/6 = 3⅓ मिनट;
कुल समय = 10 + 3⅓ = 13⅓ मिनट।

29. A alone can do a work in 25 days. B alone can do the same work in 15 days. They work alternately starting with A. How long will the work take? (A अकेले 25 दिन, B 15 दिन में काम करता है। वे बारी-बारी से काम करते हैं, A से शुरू करते हुए। पूरा काम कब होगा?)

Answer: Work/day A = 1/25, B = 1/15;
Work in 2 days (A+B) = 1/25 + 1/15 = (3+5)/75 = 8/75;
Work done in n cycles of 2 days = n × 8/75;
After 9 cycles (18 days), work done = 9 × 8/75 = 72/75 = 24/25;
Remaining = 1/25;
Next day A works and finishes remaining work in 1 day;
Total time = 18 + 1 = 19 days.

उत्तर: A का दैनिक कार्य = 1/25, B = 1/15;
2 दिन में कार्य (A+B) = 1/25 + 1/15 = (3+5)/75 = 8/75;
n चक्र में कार्य = n × 8/75;
9 चक्र (18 दिन) में कार्य = 9 × 8/75 = 72/75 = 24/25;
बचा = 1/25;
अगला दिन A काम करता है और 1 दिन में पूरा करता है;
कुल समय = 18 + 1 = 19 दिन।

30. A, B, and C can do a work in 6, 8, and 12 days respectively. They work together for 2 days. Then C leaves, and A and B continue. How many days in total will it take to finish the work? (A, B, C क्रमशः 6, 8, 12 दिनों में काम करते हैं। वे 2 दिन मिलकर काम करते हैं, फिर C छोड़ देता है। कुल कितने दिन लगेंगे?)

Answer: Work/day A+B+C = 1/6 + 1/8 + 1/12 = (4+3+2)/24 = 9/24 = 3/8;
Work done in 2 days = 2 × 3/8 = 3/4;
Remaining work = 1 – 3/4 = 1/4;
Work/day A+B = 1/6 + 1/8 = (4+3)/24 = 7/24;
Time by A+B to finish = (1/4) ÷ (7/24) = (1/4) × (24/7) = 6/7 days ≈ 0.86 days;
Total time = 2 + 0.86 ≈ 2.86 days.

उत्तर: A+B+C दैनिक कार्य = 1/6 + 1/8 + 1/12 = (4+3+2)/24 = 9/24 = 3/8;
2 दिन में कार्य = 2 × 3/8 = 3/4;
बचा कार्य = 1 – 3/4 = 1/4;
A+B दैनिक कार्य = 1/6 + 1/8 = (4+3)/24 = 7/24;
A+B का समय = (1/4) ÷ (7/24) = (1/4) × (24/7) = 6/7 दिन ≈ 0.86 दिन;
कुल समय = 2 + 0.86 ≈ 2.86 दिन।

31. A can do a work in 20 days, B in 25 days. They work together for 5 days, then B leaves. How long will A take to finish the remaining work? (A 20 दिन, B 25 दिन में काम करता है। वे 5 दिन मिलकर काम करते हैं, फिर B छोड़ देता है। A बचा काम कब पूरा करेगा?)

Answer: Work/day A+B = 1/20 + 1/25 = (5+4)/100 = 9/100;
Work done in 5 days = 5 × 9/100 = 45/100 = 9/20;
Remaining work = 1 – 9/20 = 11/20;
A alone rate = 1/20;
Time by A = (11/20) ÷ (1/20) = 11 days;
Total time = 5 + 11 = 16 days.

उत्तर: A+B का दैनिक कार्य = 1/20 + 1/25 = (5+4)/100 = 9/100;
5 दिन में किया गया कार्य = 5 × 9/100 = 45/100 = 9/20;
बचा कार्य = 1 – 9/20 = 11/20;
A की दर = 1/20;
A का समय = (11/20) ÷ (1/20) = 11 दिन;
कुल समय = 5 + 11 = 16 दिन।

32. A is 50% more efficient than B. If A can do a work in 20 days, how long will B take? (A, B से 50% अधिक कुशल है। A 20 दिन में काम करता है। B कितना दिन लेगा?)

Answer: Efficiency ratio A:B = 3:2;
Time ratio B:A = 3:2;
If A takes 20 days, B takes (3/2) × 20 = 30 days.

उत्तर: दक्षता अनुपात A:B = 3:2;
समय अनुपात B:A = 3:2;
यदि A 20 दिन लेता है, तो B = (3/2) × 20 = 30 दिन।

33. Two people can do a work in 15 days. One of them is twice as efficient as the other. Find the time taken by each. (दो लोग 15 दिनों में काम करते हैं। एक दूसरे से दोगुना कुशल है। दोनों कितना समय लेंगे?)

Answer: Let slower person take x days, faster takes x/2 days;
Work/day slower = 1/x, faster = 2/x;
Together = 1/x + 2/x = 3/x = 1/15;
So x = 45 days;
Slower = 45 days, faster = 22.5 days.

उत्तर: मान लें धीमा व्यक्ति = x दिन, तेज = x/2 दिन;
धीमे का दैनिक कार्य = 1/x, तेज का = 2/x;
साथ में = 3/x = 1/15;
तो x = 45 दिन;
धीमा = 45 दिन, तेज = 22.5 दिन।

34. A can do a work in 12 days, B in 15 days, C in 20 days. They work together for 3 days. Then A leaves. How long will B and C take to finish the remaining work? (A 12 दिन, B 15 दिन, C 20 दिन में काम करते हैं। 3 दिन मिलकर काम किया, फिर A छोड़ गया। B और C बचा काम कब पूरा करेंगे?)

Answer: Work/day A+B+C = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 12/60 = 1/5;
Work done in 3 days = 3 × 1/5 = 3/5;
Remaining work = 2/5;
Work/day B+C = 1/15 + 1/20 = (4+3)/60 = 7/60;
Time taken = (2/5) ÷ (7/60) = (2/5) × (60/7) = 24/7 ≈ 3.43 days.

उत्तर: A+B+C दैनिक कार्य = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 12/60 = 1/5;
3 दिन में किया गया कार्य = 3 × 1/5 = 3/5;
बचा कार्य = 2/5;
B+C का दैनिक कार्य = 1/15 + 1/20 = (4+3)/60 = 7/60;
समय = (2/5) ÷ (7/60) = (2/5) × (60/7) = 24/7 ≈ 3.43 दिन।

35. Two pipes fill a tank in 15 and 20 minutes respectively. A tap empties the tank in 30 minutes. If all are opened together, how long will it take to fill the tank? (दो पाइप 15 और 20 मिनट में टंकी भरते हैं। एक नल टंकी 30 मिनट में खाली करता है। यदि सभी एक साथ खोलें तो टंकी कब भरेगी?)

Answer: Filling rate = 1/15 + 1/20 = (4+3)/60 = 7/60 per minute;
Emptying rate = 1/30 per minute;
Net filling rate = 7/60 – 1/30 = 7/60 – 2/60 = 5/60 = 1/12 per minute;
Time to fill = 1 ÷ (1/12) = 12 minutes.

उत्तर: भरने की दर = 1/15 + 1/20 = (4+3)/60 = 7/60 प्रति मिनट;
खाली करने की दर = 1/30 प्रति मिनट;
शुद्ध भरने की दर = 7/60 – 1/30 = 7/60 – 2/60 = 5/60 = 1/12 प्रति मिनट;
भरने का समय = 1 ÷ (1/12) = 12 मिनट।

36. A can do a work in 10 days, B in 12 days, and C in 15 days. They start together but C leaves after 3 days. How long will A and B take to finish the remaining work? (A 10 दिन, B 12 दिन, C 15 दिन में काम करते हैं। वे साथ शुरू करते हैं, C 3 दिन बाद छोड़ देता है। A और B बचा काम कब पूरा करेंगे?)

Answer: Work/day A+B+C = 1/10 + 1/12 + 1/15 = (6+5+4)/60 = 15/60 = 1/4;
Work done in 3 days = 3 × 1/4 = 3/4;
Remaining work = 1/4;
Work/day A+B = 1/10 + 1/12 = (6+5)/60 = 11/60;
Time by A+B = (1/4) ÷ (11/60) = (1/4) × (60/11) = 15/11 ≈ 1.36 days;
Total time = 3 + 1.36 ≈ 4.36 days.

उत्तर: A+B+C दैनिक कार्य = 1/10 + 1/12 + 1/15 = (6+5+4)/60 = 15/60 = 1/4;
3 दिन में किया गया कार्य = 3 × 1/4 = 3/4;
बचा कार्य = 1/4;
A+B का दैनिक कार्य = 1/10 + 1/12 = (6+5)/60 = 11/60;
A+B का समय = (1/4) ÷ (11/60) = (1/4) × (60/11) = 15/11 ≈ 1.36 दिन;
कुल समय = 3 + 1.36 ≈ 4.36 दिन।

37. A can complete a work in 24 days, B in 30 days. They work on alternate days starting with A. How long will it take to finish the work? (A 24 दिन, B 30 दिन में काम करता है। वे वैकल्पिक दिनों में काम करते हैं, A से शुरू करते हैं। काम पूरा होने में कितना समय लगेगा?)

Answer: Work/day A = 1/24, B = 1/30;
Work in 2 days (A+B) = 1/24 + 1/30 = (5+4)/120 = 9/120 = 3/40;
After 26 days (13 cycles), work done = 13 × 3/40 = 39/40;
Remaining work = 1 – 39/40 = 1/40;
On 27th day A works and completes 1/24 work, which is more than 1/40;
So total time ≈ 26 + (1/40) ÷ (1/24) = 26 + (1/40) × 24 = 26 + 0.6 = 26.6 days.

उत्तर: A का दैनिक कार्य = 1/24, B का = 1/30;
2 दिन का कार्य (A+B) = 1/24 + 1/30 = (5+4)/120 = 9/120 = 3/40;
26 दिन में (13 चक्र) किया गया कार्य = 13 × 3/40 = 39/40;
बचा कार्य = 1 – 39/40 = 1/40;
27वें दिन A काम करेगा और 1/24 कार्य करेगा, जो 1/40 से अधिक है;
कुल समय ≈ 26 + (1/40) ÷ (1/24) = 26 + (1/40) × 24 = 26 + 0.6 = 26.6 दिन।

38. A does 60% of a work in 12 days. How long will he take to complete the whole work? (A 12 दिन में 60% काम करता है। पूरा काम कितना समय लेगा?)

Answer: 60% work = 12 days;
1% work = 12 ÷ 60 = 0.2 days;
100% work = 0.2 × 100 = 20 days.

उत्तर: 60% काम = 12 दिन;
1% काम = 12 ÷ 60 = 0.2 दिन;
100% काम = 0.2 × 100 = 20 दिन।

39. A and B together can do a work in 18 days. If A alone can do it in 30 days, how long will B alone take? (A और B मिलकर 18 दिन में काम करते हैं। A अकेला 30 दिन में करता है। B अकेला कितने दिन लेगा?)

Answer: Work/day A+B = 1/18, A = 1/30;
B = 1/18 – 1/30 = (5 – 3)/90 = 2/90 = 1/45;
So B alone takes 45 days.

उत्तर: A+B का दैनिक कार्य = 1/18, A का = 1/30;
B = 1/18 – 1/30 = (5 – 3)/90 = 2/90 = 1/45;
अतः B अकेला 45 दिन लेगा।

40. A, B and C can do a work in 12, 15 and 20 days respectively. They start together, but B leaves after 4 days and C after 6 days. How long will A take to finish the work? (A, B, C क्रमशः 12, 15, 20 दिन में काम करते हैं। वे साथ शुरू करते हैं, B 4 दिन बाद, C 6 दिन बाद छोड़ देता है। A पूरा काम कब करेगा?)

Answer: Work/day A = 1/12, B = 1/15, C = 1/20;
Work done by A in total days = x days;
Work done in first 4 days by A+B+C = 4 × (1/12 + 1/15 + 1/20) = 4 × (5+4+3)/60 = 4 × 12/60 = 4 × 1/5 = 4/5;
Work done in next 2 days by A+C = 2 × (1/12 + 1/20) = 2 × (5+3)/60 = 2 × 8/60 = 2 × 2/15 = 4/15;
Total work done so far = 4/5 + 4/15 = (12/15 + 4/15) = 16/15 (more than 1, so work finishes before 6 days.)
Let A work total t days, then:
Work by A till finish = (1/12) × t;
Work by B for 4 days = 4 × 1/15 = 4/15;
Work by C for y days = y × 1/20;
Total work = 1;
Since B leaves after 4 days and C after y days (≤6), but from above, we assume C leaves exactly after 6 days:
Work done = A’s work in t days + B’s 4 days + C’s 6 days = 1;
(1/12)t + 4/15 + 6/20 = 1;
(1/12)t + 4/15 + 3/10 = 1;
(1/12)t = 1 – 4/15 – 3/10 = 1 – 8/30 – 9/30 = 1 – 17/30 = 13/30;
t = (13/30) × 12 = 13 × (12/30) = 13 × 0.4 = 5.2 days.

उत्तर: A का दैनिक कार्य = 1/12, B = 1/15, C = 1/20;
पहले 4 दिन A+B+C का कार्य = 4 × (1/12 + 1/15 + 1/20) = 4 × 12/60 = 4 × 1/5 = 4/5;
अगले 2 दिन A+C का कार्य = 2 × (1/12 + 1/20) = 2 × 8/60 = 4/15;
कुल कार्य = 4/5 + 4/15 = 16/15 (1 से अधिक, तो 6 दिन से पहले पूरा होगा);
मान लें A ने कुल t दिन काम किया;
B 4 दिन काम करता है = 4/15;
C 6 दिन काम करता है = 6/20 = 3/10;
कुल कार्य = 1/12 × t + 4/15 + 3/10 = 1;
1/12 t = 1 – 4/15 – 3/10 = 13/30;
t = 13/30 × 12 = 5.2 दिन।

41. A is twice as efficient as B and can complete a work in 10 days less than B. How many days will they take to complete the work together? (A, B से दोगुना कुशल है और B से 10 दिन कम में काम पूरा करता है। दोनों मिलकर काम कितने दिन में पूरा करेंगे?)

Answer: Let B take x days; A takes x-10 days;
Efficiency of A = 1/(x-10), B = 1/x;
Together = 1/(x-10) + 1/x = x + (x-10)/(x(x-10));
Together’s time = x(x-10)/(2x-10).

उत्तर: मान लें B = x दिन, A = x-10 दिन;
A की दक्षता = 1/(x-10), B = 1/x;
साथ में = x + (x-10)/(x(x-10));
समय = x(x-10)/(2x-10)।

42. A can complete a work in 15 days, while B can complete the same work in 10 days. They work together for 5 days. How much work is left? (A 15 दिन, B 10 दिन में काम करता है। दोनों 5 दिन मिलकर काम करते हैं। कितना काम बचा है?)

Answer: Work/day A = 1/15, B = 1/10;
Together = 1/15 + 1/10 = (2+3)/30 = 1/6;
Work done in 5 days = 5 × 1/6 = 5/6;
Remaining work = 1 – 5/6 = 1/6.

उत्तर: A का दैनिक कार्य = 1/15, B = 1/10;
साथ में = 1/15 + 1/10 = 1/6;
5 दिन में किया गया कार्य = 5 × 1/6 = 5/6;
बचा कार्य = 1 – 5/6 = 1/6।

43. A does 3/5th of a work in 6 days. How many more days will he take to complete the work? (A 6 दिन में काम का 3/5 भाग करता है। पूरा काम करने में उसे और कितने दिन लगेंगे?)

Answer: Time for 3/5 work = 6 days;
Time for 1 work = 6 × (5/3) = 10 days;
Remaining work time = 10 – 6 = 4 days.

उत्तर: 3/5 काम में समय = 6 दिन;
1 काम का समय = 6 × (5/3) = 10 दिन;
बचा कार्य = 10 – 6 = 4 दिन।

44. A pipe can fill a tank in 8 hours, and another pipe can empty it in 12 hours. If both pipes are opened together, how long will it take to fill the tank? (एक पाइप 8 घंटे में टंकी भरता है और दूसरा 12 घंटे में खाली करता है। दोनों खोलने पर टंकी कब भरेगी?)

Answer: Filling rate = 1/8, emptying rate = -1/12;
Net rate = 1/8 – 1/12 = (3-2)/24 = 1/24;
Time to fill = 24 hours.

उत्तर: भरने की दर = 1/8, खाली करने की दर = -1/12;
शुद्ध दर = 1/8 – 1/12 = 1/24;
भरने का समय = 24 घंटे।

45. A can do a work in 40 days, B in 60 days. They start working together, but A leaves after 10 days. How long will B take to finish the remaining work? (A 40 दिन, B 60 दिन में काम करता है। दोनों काम शुरू करते हैं, पर A 10 दिन बाद छोड़ देता है। B बचा काम कब पूरा करेगा?)

Answer: Work/day A = 1/40, B = 1/60;
Together = 1/40 + 1/60 = (3+2)/120 = 1/24;
Work done in 10 days = 10 × 1/24 = 10/24 = 5/12;
Remaining work = 1 – 5/12 = 7/12;
Time for B = (7/12) ÷ (1/60) = 35 days.

उत्तर: A का दैनिक कार्य = 1/40, B = 1/60;
साथ में = 1/40 + 1/60 = 1/24;
10 दिन में किया गया कार्य = 10 × 1/24 = 5/12;
बचा कार्य = 1 – 5/12 = 7/12;
B का समय = (7/12) ÷ (1/60) = 35 दिन।

46. A can complete a work in 25 days, B can complete the same work in 20 days. How long will it take if they work alternately starting with A? (A 25 दिन, B 20 दिन में काम करता है। वे वैकल्पिक रूप से काम करते हैं। A से शुरू करते हैं। काम कब पूरा होगा?)

Answer: Work/day A = 1/25, B = 1/20;
Work in 2 days = 1/25 + 1/20 = (4+5)/100 = 9/100;
After 11 cycles = 11 × (9/100) = 99/100;
Remaining work = 1 – 99/100 = 1/100;
A takes (1/100) ÷ (1/25) = 0.25 days;
Total time = 22 + 0.25 = 22.25 days.

उत्तर: A का दैनिक कार्य = 1/25, B = 1/20;
2 दिन में कार्य = 1/25 + 1/20 = 9/100;
11 चक्र = 11 × 9/100 = 99/100;
बचा कार्य = 1 – 99/100 = 1/100;
A का समय = (1/100) ÷ (1/25) = 0.25 दिन;
कुल समय = 22 + 0.25 = 22.25 दिन।

47. A and B can complete a task together in 10 days. A alone can do it in 15 days. How many days will B take to complete the work alone? (A और B 10 दिन में काम करते हैं। A अकेला 15 दिन में करता है। B अकेला काम कितने दिन में करेगा?)

Answer: Together = 1/10, A = 1/15;
B = 1/10 – 1/15 = (3-2)/30 = 1/30;
B alone takes 30 days.

उत्तर: साथ में = 1/10, A = 1/15;
B = 1/10 – 1/15 = 1/30;
B अकेला 30 दिन लेगा।

48. A can do a job in 50 days. B is 25% more efficient than A. How many days will B alone take to complete the job? (A 50 दिन में काम करता है। B, A से 25% अधिक कुशल है। B अकेला कितने दिन में काम करेगा?)

Answer: Efficiency of A = 1/50;
Efficiency of B = 1.25 × 1/50 = 1/40;
B takes 40 days.

उत्तर: A की दक्षता = 1/50;
B की दक्षता = 1.25 × 1/50 = 1/40;
B 40 दिन लेगा।

49. A and B together can finish a job in 12 days. B alone can do the same job in 20 days. If they are paid ₹600 for the job, what is A’s share? (A और B मिलकर 12 दिन में काम करते हैं। B अकेला 20 दिन में करता है। ₹600 की मजदूरी में A का हिस्सा कितना होगा?)

Answer: Together = 1/12, B = 1/20;
A = 1/12 – 1/20 = (5-3)/60 = 2/60 = 1/30;
Work ratio A:B = 1/30 : 1/20 = 2:3;
A’s share = (2/5) × 600 = ₹240.

उत्तर: साथ में = 1/12, B = 1/20;
A = 1/12 – 1/20 = 1/30;
कार्य अनुपात A:B = 2:3;
A का हिस्सा = (2/5) × 600 = ₹240।

50. A can complete a work in 12 days, B in 16 days, and C in 24 days. If they work together, how many days will it take to complete the work? (A 12 दिन, B 16 दिन, C 24 दिन में काम करता है। वे मिलकर काम कितने दिन में करेंगे?)

Answer: Work/day A = 1/12, B = 1/16, C = 1/24;
Together = 1/12 + 1/16 + 1/24 = (2+3+4)/48 = 9/48 = 3/16;
Time = 16/3 ≈ 5.33 days.

उत्तर: A का दैनिक कार्य = 1/12, B = 1/16, C = 1/24;
साथ में = 1/12 + 1/16 + 1/24 = 3/16;
समय = 16/3 ≈ 5.33 दिन।

Time and Work – 50 Questions with Answers (समय और कार्य – 50 प्रश्न उत्तर सहित)

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