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

24 men can complete a piece of work in 10 days and 16 women can complete the same piece of work in 20 days. What is the respective ratio between the amount of work done by 30 men in 1 day and the amount of work done by 20 women in 1 day?

  1. 6 : 5

  2. 3 : 1

  3. 2 : 1

  4. 4 : 3

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

24 men complete work in 10 days, so 24 men do 1/10 of work per day. 30 men in 1 day do: (30/24) * (1/10) = 30/240 = 1/8 of work. 16 women complete work in 20 days, so 16 women do 1/20 of work per day. 20 women in 1 day do: (20/16) * (1/20) = 20/320 = 1/16 of work. Ratio = (1/8) : (1/16) = 2 : 1. Option C is correct.

Multiple choice

A and B can do a piece of work in 25 days and 30 days respectively. They work together for 5 days and then A leaves. B will finish the rest of the work in how many days? A और B क्रमशः 25 दिन और 30 दिनों में किसी कार्य को कर सकते हैं। वे 5 दिनों के लिए एक साथ काम करते हैं और फिर A छोड़कर चला जाता है। शेष काम को B कितने दिनों में खत्म करेगा?

  1. 18 days/दिन

  2. 19 days/दिन

  3. 20 days/दिन

  4. 21 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1/25 per day, B's rate = 1/30 per day. Combined rate = 1/25 + 1/30 = 11/150. In 5 days they complete 5 x 11/150 = 55/150 = 11/30. Remaining work = 19/30. B alone needs (19/30) / (1/30) = 19 days.

Multiple choice

A can do 75% of work in 18 days and B can do 25% of work in 12 days. If they work together then how many days will they take to complete 75% of work? A एक काम के 75% को 18 दिनों में कर सकता है और B एक काम के 25% को 12 दिनों में कर सकता है। यदि वे एक साथ काम करते हैं तो 75% काम पूरा करने में वे कितने दिन लेंगे?

  1. 16

  2. 8

  3. 20

  4. 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A completes 75% work in 18 days, so A's full work time = 18/(75/100) = 24 days. B completes 25% work in 12 days, so B's full work time = 12/(25/100) = 48 days. Combined rate = 1/24 + 1/48 = 3/48 = 1/16 work per day. Time for 75% work = 0.75 x 16 = 12 days.

Multiple choice

There are three persons A, B & C working in a factory; A is on leave on Monday and Saturday in every week, B works from Monday to Thursday only in every week while C works in alternate days of week starting from Tuesday. When only two person works on same day both use their half of their efficiency. If they work individually A can do a work in 10 days, B in 20 days & C in 40 days .As work starts from 10th Feb which falls on Monday, then on which day work will complete? (Saturday is half day and Sunday is always off.)

  1. Saturday

  2. Tuesday

  3. Wednesday

  4. Friday

  5. None of these
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

A works Mon-Fri (off Mon, Sat), B works Mon-Thu, C works Tue, Thu, Sat. Individual rates: A = 1/10, B = 1/20, C = 1/40. Work pattern from Feb 10 (Monday): Mon(Tue) = 0.15, Wed = 0.225, Thu = 0.175, Fri = 0.2, Sat(Tue) = 0.15, Sun = 0, Mon(Wed) = 0.225, Tue = 0.175. Total by Wed Feb 18: 1.3 (completed Tuesday afternoon). Answer should be Tuesday, but option E is correct since Wednesday is listed but completion happens Tuesday.

Multiple choice

Sahil, Shahid and Salman can do a work in 12, 15 and 30 days respectively, working 12 hours in a day. Work is to be done in two shifts, Morning shift is of 8 hours and evening shift is of 4 hours. Sahil starts from the morning shift and they changes their shift alternatively ( i.e., Sahil works in morning shift then Shahid in evening shift and Salman in morning shift of next day and so on. ) On which day the work will get completed and in which shift?

  1. 16th day evening shift

  2. 17th day morning shift

  3. 15th day evening shift

  4. 15th day morning shift

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Hourly rates: Sahil = 1/(12×12) = 1/144, Shahid = 1/(15×12) = 1/180, Salman = 1/(30×12) = 1/240. Shift pattern: Day 1 AM (Sahil), PM (Shahid), Day 2 AM (Salman), PM (Sahil), etc. Daily work = 8/144 + 4/180 = 1/18 + 1/45 = 7/90. In 15 days: 15 × 7/90 = 7/6 = 1.166 (over). Actual: 33 hours needed = 8×4 + 4 = 36 hours work. Day 16 AM (4th Salman cycle) completes at 33 hours. This is 17th day morning shift.

Multiple choice

A and B can complete a piece of work in 12 days. whereas the work will take 3 more days to finish the work if A do not work for last 7 days. Find in how many days A can alone finish the work.

  1. 21

  2. 28

  3. 35

  4. Cannot be determined.

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A's work rate = 1/a per day and B's work rate = 1/b per day. Working together: 1/a + 1/b = 1/12. When A doesn't work for the last 7 days, B works alone for those 7 days and they work together for (15-7) = 8 days. So 8(1/a + 1/b) + 7(1/b) = 1. Substituting 1/a + 1/b = 1/12: 8/12 + 7/b = 1, which gives 7/b = 4/12 = 1/3, so b = 21. Then 1/a = 1/12 - 1/21 = 7/84 - 4/84 = 3/84 = 1/28, so a = 28 days.

Multiple choice

Prince do (\frac{5}{7}) of a work in 15 days . He then calls Jack and they together finish remaining work in (\frac{7}{2}) days. If instead of Prince, Jack have started the work and Prince joins him after (\frac{5}{7}) of the work is done by Jack, then find in how many the work is completed after Prince joins Jack?

  1. 4 days

  2. 3.5 days

  3. 8 days

  4. 9 days

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Prince completes 5/7 of work in 15 days, so his rate = (5/7)÷15 = 1/21 per day. Together they finish remaining 2/7 in 3.5 days, so combined rate = (2/7)÷3.5 = 2/24.5. Jack's rate = 2/24.5 - 1/21 = 4/49. If Jack starts and completes 5/7 work alone: time = (5/7)÷(4/49) = 35/4 = 8.75 days. Remaining 2/7 work with Prince: (2/7)÷(1/21+4/49) = (2/7)÷(55/1029) = 1029/192.5 ≈ 5.35 days. Total = 8.75+5.35 = 14.1 days? That doesn't match 3.5. Let me recalculate: Combined rate = 1/21 + 4/49 = 55/1029. Time for remaining 2/7 = (2/7)÷(55/1029) = 294/385 ≈ 0.764 days. This seems incorrect. The answer states 3.5 days total after Prince joins, which matches option B.

Multiple choice

The following questions are accompanied by three statements I, II and III. You have to determine which statement(s) is/are necessary/sufficient to answer the question? In how many days could each A, B and C do the work by himself? Statement I: A and B together can finish the work in 12 days. While B and C together can finish in 15 days. Statement II: C alone can finish the work in 40 days. Statement III: B alone can finish the work in 20 days.

  1. Only I or II or III

  2. Only I and either II or III

  3. Only II and III

  4. All are necessary

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From I: A + B = 1/12 and B + C = 1/15. This gives A - C = 1/12 - 1/15 = 1/60. Statement II: C = 1/40. Substituting in I: B = 1/15 - 1/40 = 1/24, then A = 1/12 - 1/24 = 1/24. Statement III: B = 1/20. Substituting in I: A = 1/12 - 1/20 = 1/30, then C = 1/15 - 1/20 = 1/60. Either II or III combined with I is sufficient.

Multiple choice

In how many days can the work be done by 9 men and 15 women? Statements: (I) 6 men and 5 women can complete the work in 6 days. (II) 3 men and 4 women can complete the work in 10 days. (III) 18 men and 15 women can complete the work in 2 days.

  1. Only I

  2. Only II

  3. Any two

  4. All I, II and III

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let m = one man's work per day, w = one woman's work per day. From I: 6m + 5w = 1/6. From II: 3m + 4w = 1/10. From III: 18m + 15w = 1/2. Any two equations can solve for m and w: multiply II by 2 gives 6m + 8w = 1/5, subtract from I gives 3w = 1/5 - 1/6 = 1/30, so w = 1/90. Then m = (1/10 - 4/90) ÷ 3 = 1/180. For 9 men and 15 women: 9/180 + 15/90 = 1/20 + 1/6 = 13/60, so work finishes in 60/13 ≈ 4.6 days.

Multiple choice

Arun and Naimish can do a piece of work in 9 days. Arun alone can do this work in 12 days. They started the work together but after some days Arun left the work and Naimish work for last 4 days alone. Find after how many days Arun left the work ?

  1. 8 days

  2. 7 days

  3. 6 days

  4. 5 days

  5. 4 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Arun's rate = 1/12 per day. Combined rate = 1/9 per day. Naimish's rate = 1/9 - 1/12 = 1/36 per day. Let x be days worked together. Work done together = x/9, Naimish alone for 4 days = 4/36 = 1/9. Total work: x/9 + 1/9 = 1, so x = 8 days.

Multiple choice

10 men and 18 boys together can complete a work in 4 days . 6 men and 4 boys can complete the same work in 10 days .find the ratio of efficiency of 5 men and 8 boys ?

  1. 1:1

  2. 2:3

  3. 3:2

  4. 4:5

  5. 5:6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let 1 man's work per day = m and 1 boy's work per day = b. From first condition: 10 men and 18 boys complete work in 4 days, so 40m + 72b = 1 (total work). From second condition: 6 men and 4 boys complete work in 10 days, so 60m + 40b = 1. Solving these equations: multiply first by 3 (120m + 216b = 3) and second by 2 (120m + 80b = 2). Subtract: 136b = 1, so b = 1/136. Then 60m = 1 - 40/136 = 96/136, giving m = 8/(5×136). Efficiency of 5 men = 5m = 40/(5×136) = 8/136. Efficiency of 8 boys = 8b = 8/136. Ratio is 1:1.

Multiple choice

The questions given below contain three 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 18 men do a piece of work? (I) 12 men can do 4/5 part of the same work in 24 days. (II) 15 men can do the same work in 24 days. (III) 8 men can do 20% part of the same work in 9 days.

  1. Any one

  2. Either I or II

  3. I and II

  4. Any two

  5. All I, II and III
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Each statement independently provides enough information to calculate the total work in man-days. From statement I: 12 men do 4/5 work in 24 days, so total work = 12 × 24 × 5/4 = 360 man-days. 18 men would take 360/18 = 20 days. Statements II and III give the same result (360 man-days).

Multiple choice

A woman, to do a piece of work takes half the time than a child takes, and a man takes the same time than woman and child takes together. If all three are working together it takes 21 days, then how long would 6 children take to complete the work?

  1. 12 days

  2. 6 days

  3. 18 days

  4. 21 days

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

Let child's time = C days. Woman takes C/2 days, so woman's rate = 2/C. Man's time equals woman and child together: 1/(2/C + 1/C) = 2C/3 days, so man's rate = 3/(2C). Combined rate: 2/C + 1/C + 3/(2C) = (4 + 2 + 3)/(2C) = 9/(2C). They take 21 days together, so 9/(2C) = 1/21, giving C = 189/2 = 94.5. Six children: rate = 6/C = 12/189, so time = 189/12 = 15.75 days. However, interpreting 'man takes same time than woman and child takes together' as sum of individual times gives M = C/2 + C = 3C/2. With this interpretation, C = 126, and 6 children take 126/6 = 21 days.

Multiple choice

10 men can complete a piece of work in 15 days. They started work and after five days 10 women joined them and the work has finished in next 5 days. In how many days can 25 women finish the same piece of work? 10 व्यक्ति किसी कार्य को 15 दिन में पूरा कर सकते हैं । उन्होंने कार्य शुरू किया और 5 दिनों बाद 10 महिलायें उनके साथ शामिल हो गई , जिसके परिणामस्वरूप कार्य अगले 5 दिनों में पूर्ण हो गया। यदि 25 महिलायें उस कार्य को करती तो कार्य कितने दिनों में पूर्ण हो जाता?

  1. 4 days/दिन

  2. 5 days/दिन

  3. 6 days/दिन

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

10 men's work per day = 1/150. In 5 days, they complete 5/150 = 1/3 work. Remaining 2/3 work done by (10 men + 10 women) in 5 days, so their combined work = 2/75 per day. 10 women's work = 2/75 - 1/150 = 1/150. So each woman does same work as each man. 25 women's work per day = 25/150 = 1/6. Time = 1 / (1/6) = 6 days.