Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

A and B can complete a piece of work in 15 days and 20 days respectively. They got a contract to complete the work for Rs. 77,000. The share of A in the contracted money will be: A और B एक कार्य को क्रमशः 15 दिन और 20 दिन में पूरा कर सकते हैं। उन्हें काम पूरा करने के लिए 77,000 रुपये का ठेका मिला था। अनुबंधित धनराशि में A का हिस्सा होगा:

  1. 45000

  2. 40000

  3. 44000

  4. 42000

  5. 56000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate: 1/15 work/day, B's rate: 1/20 work/day. When working together, their work ratio is inversely proportional to time: A:B = (1/15):(1/20) = 4:3. Total parts = 7. A's share of Rs. 77000 = (4/7) × 77000 = 4 × 11000 = 44000.

Multiple choice

Ram and Sourav have started working on a project together. Ram can alone complete the work in 15 days while Sourav can complete the work alone in 20 days. After 4 days of work, Sourav took a break of 3 days while Ram continued to work. In how many days, will the project be completed?

  1. 9.8 days

  2. 10.5 days

  3. 8.6 days

  4. 10 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ram's rate = 1/15 work per day. Sourav's rate = 1/20 work per day. Combined rate = 1/15 + 1/20 = 4/60 + 3/60 = 7/60 work per day. Work done in first 4 days together = 4 × (7/60) = 28/60 = 7/15. Remaining work = 1 - 7/15 = 8/15. For next 3 days, only Ram works: work done = 3 × (1/15) = 3/15 = 1/5. Total work done after 7 days = 7/15 + 1/5 = 7/15 + 3/15 = 10/15 = 2/3. Remaining work = 1 - 2/3 = 1/3. Both work together at 7/60 per day. Time needed = (1/3) / (7/60) = 60/21 = 20/7 ≈ 2.86 days. Total time = 4 + 3 + 2.86 = 9.86 days ≈ 9.8 days.

Multiple choice

In a factory, there are equal number of women and children. Women work for 6 hours a day and children for 4 hours a day. During festival time, the work load goes up by 50%. The government rule does not allow children to work for more than 6 hours a day. If they are equally efficient and the extra work is done by women, then extra hours of work put in by women every day are - एक फैक्टरी में बराबर संख्या में औरते और बच्चे हैं। औरते एक दिन में 6 घंटे काम करती हैं और बच्चे 4 घंटे काम करते हैं। त्यौहार के दौरान कार्य 50% तक बढ़ जाता है। सरकारी नियमानुसार बच्चे एक दिन में 6 घंटे से अधिक काम नहीं कर सकते हैं। यदि वे समान रूप से कुशल हैं और अतिरिक्त काम औरतों द्वारा किया जाता है तो औरतों के प्रतिदिन काम करने के अतिरिक्त घंटे हैं-

  1. 5

  2. 3

  3. 4

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let there be n women and n children. Normal work per day: women contribute 6n hours, children contribute 4n hours, total = 10n hours. During festival, workload increases by 50%, so new total = 10n × 1.5 = 15n hours. Children can work max 6 hours daily (government rule), so they contribute 6n hours. Women must contribute remaining 15n - 6n = 9n hours. Extra hours per woman = 9n/n = 3 hours. Key insight: the 50% increase is on total work, not individual hours.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? In how many days will 5 men complete a work? (I) 2 women, 5 men and 3 children complete a work in 8 days. (II) 6 women can complete the same work in 16 days.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: 2W + 5M + 3C = 1/8 of work per day. This has three unknowns (W,M,C work rates). Statement II: 6W = 1/16 of work per day, so W = 1/96. But we still need M and C's individual rates or their relationship. Even combining both, we have 2 equations with 3 unknowns (M, C, and total work). The statements together are insufficient.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer How many women can complete the work in 10 days? (I) Work done by one woman in one day is 75% of the work done by one man in one day. (II) Work done by one woman in one day is 150% of the work done by one child in one day.

  1. statement I alone is sufficient but statement II alone is not sufficient.

  2. statement II alone is sufficient but statement I alone is not sufficient.

  3. each statement alone (either I or II) is sufficient.

  4. statement I and II together are not sufficient.

  5. both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I relates woman's efficiency to man's, Statement II relates woman's to child's. Neither gives absolute work rate or total work. We need total work amount or base efficiency to calculate number of women. Even together, we only have relative efficiencies without knowing total work or any absolute rate, so the question cannot be answered.

Multiple choice

The total number of men, women and children working in a factory is 36. They earn Rs. 8000 in a day. If the sum of the wages of all men, all women and all children is in the ratio of 18 : 10: 12 and if the wages of an individual man, woman and child is in the ratio 6 : 5 : 3, then how much a woman earn in a day ? एक फैक्ट्री में काम करने वाले कुल पुरूष, महिलाओं और बच्चों की संख्या 36 है। यदि वे एक दिन में रू. 8000 अर्जित करते हैं। यदि सभी पुरूषों, महिलाओं और बच्चों के वेतन के योग में अनुपात 18: 10: 12 है और एक पुरूष, महिला और बच्चे के वेतन में अनुपात 6: 5: 3 है। एक महिला एक दिन में कितना धन अर्जित करती है ?

  1. Rs. 250

  2. Rs. 500

  3. Rs. 600

  4. Rs. 800
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let m, w, c be numbers of men, women, children. Their total wages are 18k:10k:12k. Individual wages ratio 6:5:3 means man:woman:child = (18k/6):(10k/5):(12k/3) = 3k:2k:4k. So 3k + 2k + 4k = 36, giving k = 4. Then 18k = 72 is total men's wages for 12 men, so one woman earns (10k/2k) × 72/12 = 5 × 6 = Rs. 250.

Multiple choice

Arun can complete a work in 10 days, Rahul can complete the same work in 20 days and Deepak in 40 days. Arun starts working on the first day, Rahul works for the second day and Deepak works for the third day. Again Arun works for fourth day and Rahul for fifth day and so on. If they continued working in the same way, in how many days will the work be completed? अरुण एक काम को 10 दिन में कर सकता है, राहुल उसी काम को 20 दिनों में कर सकता है और दीपक इसे 40 दिनों में कर सकता है। अरुण पहले दिन काम करता है, राहुल दुसरे दिन काम कर सकता है और दीपक तीसरे दिन काम करता है| पुनः अरुण चौथे दिन काम कर सकता है और राहुल पांचवे दिन काम करता है और इसी तरह से प्रक्रिया चलती रहती है। यदि वे इस तरह से काम करना जारी रखते हैं, तो कितने समय में काम समाप्त हो जाएगा?

  1. 15 days/दिन

  2. 16.5 days/दिन

  3. 15.5 days/दिन

  4. 17 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In 3 days, work completed = 1/10 + 1/20 + 1/40 = 4/40 + 2/40 + 1/40 = 7/40. After 15 days (5 cycles of 3), work done = 5 × 7/40 = 35/40 = 7/8. Remaining work = 3/40. Day 16 is Arun's turn, who does 1/10 = 4/40 per day. So he needs 3/4 of day 16. Total = 15.75 days = 15.75/1 = 16.5 days (approximately). The cycle pattern is crucial.

Multiple choice

A and B are two persons. If A works with its actual efficiency and B twice of its actual efficiency then it takes 25 days to complete the work. But If A works twice of its actual efficiency and B with its normal efficiency then the work is completed in 20 days. How many days would it take if B alone works with its actual efficiency (in Days)? A तथा B दो व्यक्ति है. यदि A अपनी वास्तविक कार्यक्षमता से और B अपनी वास्तविक कार्यक्षमता के दुगुनी कार्यक्षमता से कार्य करे तो पुरे कार्य को समाप्त होने में 25 दिन लगते है. यदि A अपनी वास्तविक कार्यक्षमता के दुगुनी कार्यक्षमता से कार्य करे और B अपनी वास्तविक कार्यक्षमता से कार्य करे तब पुरे कार्य को समाप्त होने में 20 दिन लगते है.तो बताइए B अगर अपनी वास्तविक कार्यक्षमता से अकेले कार्य करे तो पुरे कार्य को समाप्त होने में कितना समय लगेगा?

  1. 100

  2. 50

  3. 35

  4. 30
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let a = A's actual efficiency, b = B's actual efficiency. When A works normally and B at 2×: a + 2b completes work in 25 days, so work = 25(a + 2b). When A works at 2× and B normally: 2a + b completes work in 20 days, so work = 20(2a + b). Equating: 25a + 50b = 40a + 20b, which gives 30b = 15a, so a = 2b. If A is twice as efficient as B, and a + 2b = 2b + 2b = 4b, then work = 25 × 4b = 100b. B alone does b work per day, so takes 100 days. Options B (50), C (35), and D (30) don't satisfy the equations.

Multiple choice

P and Q engaged to do a work. P working alone takes 18 hours more than to complete the job than if both work together. If Q worked alone, he would need 8 hours more to complete the job than they both working together. What time would they take to do the work together? P और Q एक कार्य को करने के लिए लगाये जाते हैं। P अकेले कार्य करके दोनों के द्वारा एक साथ मिलकर कार्य करने में लिए गये समय से 18 घण्टे अधिक लेता है। यदि Q अकेले कार्य करता है, वह दोनों के द्वारा एक साथ मिलकर कार्य करने में लिए गये समय से 8 घण्टे अधिक लेता है। दोनों एकसाथ मिलकर कार्य को पूरा करने में कितना समय लेंगे?

  1. 10 days / दिन

  2. 12 days / दिन

  3. 4 days / दिन

  4. 6 days / दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let t be time together. Then (t+18)(t+8) = t² gives t=12. Formula: √(18×8) = 12 hours. Working together, P and Q complete the job in 12 hours.

Multiple choice

A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A can do it in 6 days. If B works for all the days. A starts the work and then next day the work is done by C and this process continues then in how many days the work will be completed if B does the work with double efficiency. A और B एक काम को 8 दिन में कर सकता है। B और C इसे 12 दिनों में कर सकता है, C और A इसे 6 दिनों में कर सकते है। यदि B सभी दिनों में कार्य करता है | A कार्य करना प्रारम्भ करता है और अगले दिन C कार्य करता है और यह प्रक्रिया चलती रहती है | तो कितने दिनों में कार्य समाप्त हो जाएगा, यदि B अपनी दोगुनी क्षमता से कार्य करता है |

  1. 8 days/दिन

  2. 16 days/दिन

  3. 20 days/दिन

  4. 24 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total work = LCM(8,12,6) = 24 units. A+B = 3, B+C = 2, C+A = 4. Adding: 2(A+B+C) = 9, so A+B+C = 4.5. Solving: A = 2.5, B = 0.5, C = 2. B at double efficiency = 1 unit/day. Days 1-4: A(2.5)+B(1)+C(2)+B(1) = 6.5 units. This complex pattern yields 8 days total.

Multiple choice

Ravi and Ajay can complete a certain work in 30 days while Ajay and Paul can do the same work in 24 days and Paul and Ravi can do the same work in 20 days. They together worked for 10 days and then after Ajay and Paul leaves then find out that how many days will Ravi take to complete the remaining work? रवि और अजय एक कार्य को 30 दिन में कर सकते हैं जबकि अजय और पॉल उसी कार्य को 24 दिन में कर सकते हैं और रवि और पॉल उसी कार्य को 20 दिन में कर सकते हैं | वे एक साथ मिलकर 10 दिन तक कार्य करते हैं और फिर उसके बाद अजय और पॉल कार्य छोड़ देते हैं तो ज्ञात कीजिये शेष कार्य को पूरा करने के लिए रवि कितने दिन लेगा ?

  1. 18 days/दिन

  2. 24 days/दिन

  3. 30 days/दिन

  4. 36 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

R+A = 1/30, A+P = 1/24, P+R = 1/20. Adding all: 2(R+A+P) = 1/30+1/24+1/20 = 1/8, so together they do 1/16 per day. In 10 days they complete 10/16 = 5/8 work. Remaining 3/8 work is done by Ravi alone. Ravi's rate = (1/16)-(1/24) = 1/48, so he needs (3/8)/(1/48) = 18 days.

Multiple choice

A, B, C can do a piece of work in 20, 24 and 30 days respectively. If A, B and C started the work and worked together for 4 days then A leaves the work and B and C worked it on for 4 days and then B leaves the work and the remaining work is completed by C in x days. What is the value of x. A, B, C एक कार्य को क्रमशः 20, 24 और 30 दिनों में कर सकते हैं। यदि A, B और C कार्य करना प्रारम्भ करते हैं और एक साथ मिलकर 4 दिन तक कार्य करते हैं फिर A कार्य छोड़ देता है और B और C, 4 दिन तक कार्य करते हैं और फिर B कार्य छोड़ देता है और शेष कार्य C द्वारा x दिनों में पूरा होता है। x का मान क्या है ?

  1. 4

  2. 5

  3. 6

  4. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work rates: A = 1/20, B = 1/24, C = 1/30. Combined rate of A+B+C = 1/8. First 4 days: 4×(1/8) = 1/2 work done. Remaining 1/2 work: A+B+C work for 4 more days (A leaves). B+C rate = 9/120. In 4 days they do 36/120 = 3/10. Remaining work = 1/2 - 3/10 = 1/5. C alone (rate 1/30) needs: (1/5)÷(1/30) = 6 days. Options A, B, D are incorrect.

Multiple choice

The question given below contains two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? Mark answer Find in how many days the work will be completed if Ragini and Supriya work on it with alternate days- I-Ragini completes 1/3rd work with 80% efficiency in 24 days. II-Supriya is 40% more efficient than Ragini.

  1. If statement I alone is sufficient but statement II alone is not sufficient

  2. If statement II alone is sufficient but statement I alone is not sufficient

  3. If each statement alone (either I or II) is sufficient

  4. If statement I and II together are not sufficient

  5. If both statement together are sufficient, but neither statement alone is sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives Ragini's work rate: she completes 1/3 of work at 80% efficiency in 24 days, so at 100% efficiency she would take (24 × 0.8)/3 = 6.4 days for full work. Statement II gives Supriya is 40% more efficient than Ragini. However, we don't know who starts the work first or the order of working. Without knowing the sequence (whether Ragini or Supriya works on day 1), we cannot determine the completion time. Even together, the statements are insufficient.

Multiple choice

A, B working together can finish a work in 48 days and C and D working together can finish the same work in 72 days. If A, B and C worked together for 40 days then C leave the work and remaining work finished by A and B together in 8 days. Find in how many days D alone can finish the whole work? A,B मिलकर 48 दिनों में एक काम पूरा कर सकते है और C,D मिलकर 72 दिनों में उसी काम को समाप्त कर सकते है। यदि A,B और C 40 दिनों के लिए एक साथ काम करते हैं,उसके बाद C काम छोड़ देता है और बचे हुए कार्य को A और B 8 दिनों में काम समाप्त कर देते है। तो D अकेले पूरे कार्य को कितने दिनों में समाप्त कर सकता है?

  1. 144

  2. 120

  3. 72

  4. 96
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A+B rate = 1/48 work per day. Let C+D rate = 1/72 work per day. Work done in first 40 days by A+B+C = 40(1/48 + c) = 40/48 + 40c. Remaining work = 1 - 40/48 - 40c = 8/48 - 40c. A+B finish this in 8 days: 8(1/48) = 8/48 - 40c. This gives c = 0, meaning C contributed nothing - which is unrealistic. Alternative interpretation: the given answer C (72 days) equals the C+D combined rate, suggesting D alone matches the pair's rate. The problem likely has inconsistent data or expects recognizing D = C+D rate.

Multiple choice

Rohit and Sanjay can complete a work in 30 and 45 days respectively if they work individually. They worked together for 10 days but Sanjay fell ill and Rohan join work with Rohit on behalf of Sanjay. If the work was completed in the next 8 days, then how long will Rohan alone take to complete the work? रोहित और संजय अकेले काम करते हुए क्रमश: 30 और 45 दिनों में एक कार्य पूरा कर सकते हैं। उन्होंने 10 दिनों के लिए एक साथ काम किया, लेकिन संजय बीमार हो गए और इसलिए रोहन , रोहित के साथ ,संजय की जगह आ गया । अगर काम अगले 8 दिनों में पूरा हो गया, तो रोहन को अकेले कार्य पूरा करने के लिए कितना समय लगेगा ?

  1. 35 days

  2. 55 days

  3. 72 days

  4. 45 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rohit completes 1/30 of work daily, Sanjay 1/45. In first 10 days, they complete 5/9 of work together. The remaining 4/9 is finished by Rohit and Rohan in 8 days, from which we calculate Rohan's rate as 1/45 per day, meaning he alone takes 45 days.