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

The questions 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 A and B work on it with alternate days. Statement I :- A completes 1/3rd work with 80% efficiency in 20 days. Statement II :- B is 20% more efficient than A.

  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 sufficient, but neither statement alone is sufficient

  5. If statement I and II together are not sufficient
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement I: A completes 1/3 work at 80% efficiency in 20 days. At 100% efficiency, A would complete (1/3) × (100/80) = 5/12 work in 20 days. So A's rate = (5/12)/20 = 5/240 = 1/48 work per day. Statement II: B is 20% more efficient than A, so B's rate = 1.2 × (1/48) = 1.2/48 = 1/40 work per day. However, we don't know who starts first or the order of work. The question asks about A and B working on alternate days, but doesn't specify the starting day. Without this information, we cannot determine the exact time. Even with both statements, key information is missing.

Multiple choice

Quantity I: Working alone, B can complete the work in 20 days. C is twice as efficient as B and A takes 2 days more than it takes C to complete the work. Working together, in how much time would they be able to complete 7 such works? Quantity II: Working alone, A, B and C can do a work in 24, 30 and 40 days respectively. How long will it take them to complete the work if only A and B work for the first 6 days and then C started the work?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can’t be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: B takes 20 days, so B's rate = 1/20. C is twice as efficient, so C's rate = 2/20 = 1/10 (C takes 10 days). A takes 2 days more than C, so A takes 12 days (rate = 1/12). Combined rate of A, B, C = 1/12 + 1/20 + 1/10 = 5/60 + 3/60 + 6/60 = 14/60 = 7/30. For 7 works: Time = 7 ÷ (7/30) = 30 days. Quantity II: A works for 6 days at rate 1/24, completing 6/24 = 1/4 of work. Remaining work = 3/4. With A, B, C working together at rate 1/24 + 1/30 + 1/40 = 5/120 + 4/120 + 3/120 = 12/120 = 1/10, time needed = (3/4) ÷ (1/10) = 7.5 days. Total time = 6 + 7.5 = 13.5 days. Since 30 > 13.5, Quantity I > Quantity II.

Multiple choice

The following questions are accompanied by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the questions. 4 men & 18 women can do a piece of work in 2.5 days, then in how many days 12 woman can complete the same piece of work? A. Ratio of efficiency of men to women is 3: 2. B. 6 men & 6 women can complete the same work in 4 days.

  1. Statement A alone is sufficient to answer the question but statement B alone is not sufficient to answer the questions.

  2. Statement B alone is sufficient to answer the question but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A: Ratio m:w = 3:2. From 4m+18w = 2.5 days work, can find individual rates. Then 12w time = work/12w. Statement B: 6m+6w = 4 days, gives combined rate. With A's ratio or B's data alone, each is sufficient. Answer D is correct.

Multiple choice

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values. 12 men can complete a work in 10 days. 18 women can do the same work in 20 days. 27 children can do that work in 20 days. 9 women and 9 children together do that work for 16 days. Quantity I: No. of men required to complete the remaining work in one day Quantity II: 36

  1. Quantity I > Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I = Quantity II or No relation

  4. Quantity I < Quantity II

  5. Quantity I ≥ Quantity II
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work rates: 12 men in 10 days, so 1 man's rate = 1/(120) work/day. 18 women in 20 days, so 1 woman's rate = 1/(360) work/day. 27 children in 20 days, so 1 child's rate = 1/(540) work/day. 9 women + 9 children work for 16 days: work done = 16 × (9/360 + 9/540) = 16 × (1/40 + 1/60) = 16 × (5/120) = 2/3. Remaining work = 1/3. Men needed = (1/3) / (1/120) = 40. Quantity I = 40, Quantity II = 36. Since 40 > 36, option A is correct.

Multiple choice

The question below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer. Three workers A, B and C complete a work together in 4 days. The time taken by A and B together to complete the 25% of the whole work is equal to the time taken by D and C together to complete the 150% more than the 1/10th of the whole work. In how many days, D will complete the whole work alone? Statement I: Efficiencies of A and D are in the ratio 5: 3 respectively. Statement II: Efficiencies of B and C are in the ratio 2: 3 respectively. Statement III: Efficiency of D and C are in the ratio 1: 2 respectively.

  1. Either statement I or II or III alone is sufficient.

  2. Either statement III alone is sufficient or statement I and II together are sufficient.

  3. Either statement II alone is sufficient or statement I and III together are sufficient.

  4. Either statement I and II or statement II and III together are sufficient.

  5. Any of the two statements together are sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement III alone is sufficient because it directly gives D:C efficiency ratio as 1:2. Since A+B+C complete work in 4 days, and we have the relationship between (A+B) doing 25% work and (D+C) doing 150% more than 1/10th (i.e., 25% of work), we can equate: (A+B) time = (D+C) time. This with the D:C ratio gives individual efficiencies, hence D's time alone. Statements I and II together also work: I gives A:D = 5:3, II gives B:C = 2:3, combined with the work relationship allows solving.

Multiple choice

Following questions consist a question and two statements numbered I and II. You have to decide whether the data provided in the statements are sufficient to answer the question or not. निम्नलिखित प्रश्न में एक प्रश्न और दो कथन I और II दिए गए हैं, आपको यह तय करना होगा कि कथन में दिए गए डेटा प्रश्न का उत्तर देने के लिए पर्याप्त हैं या नहीं। In how many days A and B together will complete the work? (I) A completes the work in 4 more days than A and B together takes. (II) B completes the work in 5 more days than A takes. A और B मिलकर कितने दिनों में काम पूरा करेंगे? (I) A, A और B के द्वारा लिए गए समय से 4 अधिक दिनों में कार्य पूरा करता है। (II) B, A द्वारा लिए गए समय से 5 अधिक दिनों में कार्य पूरा करता है।

  1. Only II केवल II

  2. Only I केवल I

  3. Both from I and II I और II दोनों से

  4. Any one of the two. दोनों में से कोई एक

  5. None of these. इनमें से कोई नहीं।
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A+B together take x days. Statement I: A takes x+4 days. Statement II: B takes A+5 days = x+9 days. Together: 1/x = 1/(x+4) + 1/(x+9). Solving gives x=6. Both statements needed. Option C is correct.

Multiple choice

The following questions are accompanied by three statements. You have to determine which statement (s) is/are/suffcient/ necessary to answer the question ? नीचे दिये गये प्रश्नों में तीन कथनों के माध्यम से कुछ जानकारियां दी गई है आपको यह निर्णय करना है कि क्या कथनों में दी गयी जानकारी उत्तर देने के लिए पर्याप्त है। X,Y and Z together will finish the work in how many days? (A) X does half as much work as Y and Y does half as much work as X and Z do together in one day. (B) Y does the whole work in 40 days (C) X and Z do the whole work in 20 days X, Y और Z मिलाकर एक काम को कितने दिनों में पूरा करेंगे ? (A) Y जितना कार्य एक दिन में करता है उसका आधा भाग X करता है। X और Z दोनों मिलकर जितना कार्य करते हैं Y उसका आधा भाग कार्य करता है। (B) Y अकेले पूरे कार्य को 40 दिनों में करता है। (C) X और Z दोनों मिलकर कार्य को 20 दिनों में पूरा करते हैं।

  1. All A,B & C are required A, B और C सभी कथन पर्याप्त है।

  2. A,B &C even together is not sufficient A, B और C सभी कथन पर्याप्त नहीं है।

  3. Either A or B or C sufficient या तो A या B या C पर्याप्त हैं।

  4. Either A and B together or B and C together or C and A together are sufficient. या तो A और B साथ-साथ या B और C साथ-साथ या A और C साथ-साथ पर्याप्त है।

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From statement B: Y completes work in 40 days, so Y's 1 day work = 1/40. From statement C: X and Z together complete work in 20 days, so (X+Z)'s 1 day work = 1/20. This means X and Z together are twice as efficient as Y. All three together: (X+Y+Z)'s 1 day work = 1/20 + 1/40 = 3/40. Time taken = 40/3 days. Statements B and C together are sufficient.

Multiple choice

Find the correct relationship between the given quantities: दी गई मात्राओ में सही संबंध ज्ञात कीजिये: Quantity I: P takes 5 days more than Q to finish a work. If both together can do the same job in 6 days then find sum of time taken by both of them alone to do the same work. Quantity II: A is 8/13th as efficient as B and takes 15 days more than B to finish a task. Then find the time taken by B alone to finish the same task. मात्रा I: P किसी कार्य को पूरा करने में Q से 5 दिन अधिक लेता है। यदि दोनों मिलकर 6 दिनों में पूरा कर सकते हैं, तो समान कार्य को अकेले करने के लिए, दोनों द्वारा लिये गये समय का योग ज्ञात कीजिये। मात्रा II: A की कार्य क्षमता B की कार्य क्षमता का 8/13 है तथा वह एक कार्य को पूरा करने के लिए B से 15 दिन अधिक समय लेता है।तो समान कार्य को पूरा करने के लिए B द्वारा लिया गया समय ज्ञात कीजिये।

  1. Quantity II > Quantity I मात्रा II > मात्रा I

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I > Quantity II मात्रा I > मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or the relation cannot be established संबंध स्थापित नहीं किया जा सकता या मात्रा I = मात्रा II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For Quantity I: Let Q take x days, P takes (x+5) days. Working together: 1/x + 1/(x+5) = 1/6. Solving gives x = 10, so sum = 10 + 15 = 25 days. For Quantity II: A's efficiency is 8/13 of B, so A takes 13/8 times B's time. If B takes x days, A takes (13x/8) days. Given (13x/8) - x = 15, solving gives x = 24 days. Since 25 > 24, Quantity I is greater.

Multiple choice

Find the values and state the correct relationship. मान ज्ञात कीजिये तथा सही सम्बन्ध स्थापित कीजिये। It takes (X-2) men to do a work in 2Y days and it takes (X+6) men to do the same work in Y days. Quantity I: X Quantity II: Y It takes (X-2) पुरुषों को एक कार्य करने में 2Y दिन लगते हैं और (X+6) पुरुषों को एकसमान कार्य करने में Y दिन लगते हैं। मात्रा I: X मात्रा II: Y

  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity II > Quantity I मात्रा II > मात्रा I

  4. Quantity II ≥ Quantity I मात्रा II ≥ मात्रा I

  5. Quantity I = Quantity II or Relation cannot be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता है।
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Work is constant. (X-2)×2Y = (X+6)×Y gives 2XY-4Y = XY+6Y, so XY = 10Y, meaning X=10. This only fixes X=10; Y can be any positive value. Without a second equation, Y cannot be determined uniquely, so no relationship can be established.

Multiple choice

Find the correct relationship between the given quantities: दी गई मात्राओ में सही संबंध ज्ञात कीजिये: Quantity I = Ram alone can finish a work in 60 days. In how many days Ram and Shyam together will finish the work if ratio of their efficiency is 3:2 respectively? Quantity II = In how many days Ram and Shyam together will finish the work if Ram can finish 1/5th of work in 12 days and Shyam can finish 1/3rd of work in 30 days?. मात्रा I = राम अकेले 60 दिनों में एक काम पूरा कर सकते हैं। राम और श्याम मिलकर कितने दिनों में काम खत्म करेंगे अगर उनकी दक्षता का अनुपात क्रमशः 3: 2 हो? मात्रा II = कितने दिनों में राम और श्याम एक साथ काम पूरा करेंगे अगर राम 12 दिनों में 1/5 वां काम पूरा कर सकते हैं और श्याम 30 दिनों में 1 / 3rd काम खत्म कर सकते हैं?

  1. Quantity II > Quantity मात्रा II > मात्रा I

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I > Quantity मात्रा I > मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or relationship cannot be established मात्रा I = मात्रा II या कोई संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: Ram takes 60 days alone. With efficiency ratio 3:2 (Ram:Shyam), combined efficiency = 3+2 = 5 units. Time = Total work (60*3 = 180 units) / 5 = 36 days. Quantity II: Ram does 1/5 work in 12 days, so full work in 60 days. Shyam does 1/3 work in 30 days, so full work in 90 days. Combined rate: 1/60 + 1/90 = 5/180 = 1/36, so 36 days. Both quantities equal 36 days.

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 नीचे दिए गए प्रश्नों में दो कथनों के माध्यम से कुछ जानकारियां दी गई हैं आपको यह निर्णय करना है कि क्या कथनो में दी गई जानकारी उत्तर देने के लिए पर्याप्त है। उत्तर दीजिए- Find in how many days the work will be completed if Ragini and Supriya work on it with alternate days- रागिनी और सुप्रिया एकान्तर दिनों में एक साथ कार्य करते हुए कार्य को कितने दिनों में पूरा करेंगी- I-Ragini completes 1/3rd work with 80% efficiency in 24 days. II-Supriya is 40% more efficient than Ragini who starts the work. I-रागिनी ने 24 दिनों में 80% दक्षता के साथ एक तिहाई काम पूरा किया। II-सुप्रिया, रागिनी की तुलना में 40% अधिक कुशल है जिसने कार्य प्रारम्भ किया।

  1. Only I केवल I

  2. Only II केवल II

  3. Either I or II या तो I अथवा II

  4. Both together दोनों एक साथ

  5. Both together are not sufficient दोनों एक साथ भी पर्याप्त नहीं हैं
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: Ragini does 1/3 work at 80% efficiency in 24 days, so at full efficiency she would take 24 × 0.8 × 3 = 57.6 days alone. Statement II: Supriya is 40% more efficient, so her rate = 1.4 × (1/57.6) work/day. Combined they complete work in alternate days. Day 1 (Ragini): 1/57.6 work. Day 2 (Supriya): 1.4/57.6 work. Every 2 days: 2.4/57.6 = 1/24 work. Total = 48 days. Both statements needed.

Multiple choice

12 men and 16 women together can complete a work in 26 days while 10 women and 18 children together can complete the work in 20 days. Also, 8 men and 16 children can complete the work in 25 days. 1 man, 1 woman and 1 child start the work and from 2nd day onwards every day 1 new man, 1 new woman and 1 new child join the work. On which day the work shall be completed? 12 पुरुष और 16 महिलाएं एक कार्य 26 दिनों में पूरा कर सकती हैं जबकि 10 महिलाएं और 18 बच्चे एक साथ 20 दिनों में काम पूरा कर सकते हैं। 8 पुरुष और 16 बच्चे 25 दिनों में काम पूरा कर सकते हैं। 1 आदमी, 1 महिला और 1 बच्चा कार्य शुरू करते हैं और दूसरे दिन से हर दिन 1 नया पुरुष, 1 नई महिला और 1 नया बच्चा कार्य में शामिल होते हैं। कार्य किस दिन पूरा होगा?

  1. 20th day 20 वें दिन

  2. 21st day 21 वें दिन

  3. 22nd day 22 वें दिन

  4. None of the above इनमे से कोई नहीं

  5. Cannot be determined निर्धारित नहीं किया जा सकता है
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let m,w,c be work per day by 1 man, 1 woman, 1 child. From given: 12m+16w=1/26, 10w+18c=1/20, 8m+16c=1/25. Solving the system gives m=1/5200, w=1/5200, c=1/5200 (each does equal work). Total work = 1. On day 1, work done = 3/5200. Each subsequent day adds 3 more workers, so day n completes work at rate 3n/5200. Work completed by day n = sum of 3i/5200 for i=1 to n = 3n(n+1)/(2×5200). Setting this equal to 1 and solving gives n=20.88, so work completes on day 21.

Multiple choice

Kunal can do a work in 10 days while Manish can do the same work in 20 days. They started to work together. After 3 days Kunal left the work and Manish completed it. How many days did Manish work alone for remaining work more than the number of days required when both work together to complete the work? कुनाल एक कार्य को 10 दिनों में कर सकता है जबकि मनीष उसी कार्य को 20 दिनों में कर सकता है| उन्होंने एक साथ कार्य करना प्रारंभ किया| 3 दिनों के बाद कुनाल ने कार्य छोड़ दिया और मनीष ने इसे पूरा किया| मनीष ने आवश्यक दिनों की संख्या कितने दिन अधिक अकेले कार्य किया, जिनमें उन दोनों के साथ कार्य करने पर कार्य को पूरा होना था?

  1. 5 (2/7)

  2. 7 (1/3)

  3. 6 (2/3)

  4. 4 (1/3)

  5. None of these /इनमें से को नहीं
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Kunal's rate: 1/10 work per day. Manish's rate: 1/20 work per day. Combined rate: 3/20 per day. In 3 days together: 3 × 3/20 = 9/20 work done. Remaining: 11/20. Manish does this alone at 1/20 per day, taking 11 days. Total days for Manish: 3 (together) + 11 (alone) = 14 days. If both worked together: 1/(3/20) = 20/3 = 6 2/3 days. Manish worked 14 - 6 2/3 = 7 1/3 days more. But wait - the question asks how many days Manish worked alone MORE THAN the days required when both work together. Manish alone for remaining work = 11 days. Together they'd take 6 2/3 days total. Difference: 11 - 6 2/3 = 4 1/3 days. This matches option D.

Multiple choice

Quantity I: Working alone, B can complete the work in 20 days. C is twice as efficient as B and A takes 2 days more than it takes C to complete the work. Working together, in how much time would they be able to complete 7 such works? Quantity II: Working alone, A, B and C can do a work in 24, 30 and 40 days respectively. How long will it take them to complete the work if only A and B work for the first 6 days and then C started the work? मात्रा I: अकेले कार्य करते हुए, B 20 दिनों में कार्य पूरा कर सकता है। C, B से दोगुना कुशल है और A को कार्य को पूरा करने में C से 2 दिन अधिक समय लगता है। एक साथ काम करते हुए, वे ऐसे 7 कार्यों को कितने समय में पूरा कर पाएंगे? मात्रा II: अकेले कार्य करते हुए, A, B और C क्रमशः 24, 30 और 40 दिनों में कार्य कर सकते हैं। यदि A और B पहले 6 दिनों के लिए काम करते हैं और फिर C कार्य करता है तो उन्हें काम पूरा करने में कितना समय लगेगा?

  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I < Quantity II मात्रा I < मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or relation can’t be established मात्रा I = मात्रा II या सम्बन्ध स्थापित नही किया जा सकता|
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

QI: B takes 20 days alone. C is twice efficient, so C takes 20/2 = 10 days. A takes 10+2 = 12 days. Together: 1/12 + 1/20 + 1/10 = 5/60 + 3/60 + 6/60 = 14/60 = 7/30 work/day. For 7 works: Time = 7 × 30/7 = 30 days. QII: A(24), B(30), C(40). A+B work for 6 days: 6×(1/24+1/30) = 6×(5/120+4/120) = 6×9/120 = 54/120 = 9/20 work. Remaining = 11/20. Then A+B+C together: 1/24+1/30+1/40 = 5/120+4/120+3/120 = 12/120 = 1/10. Time for remaining = (11/20) / (1/10) = 11/2 = 5.5 days. Total = 6 + 5.5 = 11.5 days. Comparing: QI = 30 days, QII = 11.5 days. QI > QII, so A is correct.

Multiple choice

30 women are employed to do a piece of work in 20 days. After 5 days, 4 men joined them and finish the work on time. If the efficiency of a man is thrice the efficiency of a woman, then find the number of days which will be required to finish the work if extra men didn't join. 30 महिलाओं को किसी कार्य को 20 दिन में पूरा करने के लिए लगाया गया। 5 दिन के पश्चात 4 पुरूष और शामिल होते हैं और कार्य वास्तविक समय पर समाप्त हो जाता है। यदि पुरूषों की कार्य क्षमता महिलाओं की तिगुनी है तो दिनों की संख्या ज्ञात कीजिए जो कार्य समाप्त करने में लगेंगे यदि अतिरिक्त पुरूषों की नियुक्ति न की जाए ।

  1. 23 days 23 दिन

  2. 32 days 32 दिन

  3. 30 days 30 दिन

  4. 26 days 26 दिन

  5. 25 days 25 दिन
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let one woman's efficiency = 1 unit/day. Total work = 30 × 20 = 600 units. In 5 days, 30 women complete 150 units. Remaining 450 units must be done in 15 days by 30 women + 4 men (12 units equivalent = 42 total). Actual rate = 450/15 = 30 units/day. Without 4 men, rate = 30 units/day, so 600 units would take 600/30 = 20 more days after day 5, totaling 26 days.