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 do a piece of work in 30 days and 45 days respectively. They start working together. After working three days A leaves and another person C joins to B. If B and C both finish the rest of work in 25/2 days then in how many days C can finish the work alone?

  1. 23⅔days

  2. 22½days

  3. 45 days

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

A and B work for 3 days: 3 * (1/30 + 1/45) = 3 * (3/90 + 2/90) = 3 * 5/90 = 1/6. Remaining work = 5/6. B and C do 5/6 in 12.5 days, so their combined rate is (5/6) / 12.5 = 1/15. Since B's rate is 1/45, C's rate is 1/15 - 1/45 = 2/45. C takes 45/2 = 22.5 days.

Multiple choice

Bharat and Priyanka can do a piece of work in 45 and 40 days respectively. They began the work together, but Bharat leaves after some days and Priyanka finished the remaining work in 23 days. After how many days did Bharat leave?

  1. 7 days

  2. 8 days

  3. 9 days

  4. 11 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Priyanka's work in 23 days = 23/40. Remaining work = 1 - 23/40 = 17/40. Bharat and Priyanka together do (1/45 + 1/40) = 17/360 per day. Days worked together = (17/40) / (17/360) = 9 days.

Multiple choice

Six men, working together all day, can finish a piece of work in 19 days, but two of them having other engagements can devote only one-half and one-quarter of their time, respectively. How long will it take for them to complete the work?

  1. 21 days

  2. 24 days

  3. 25 days

  4. 28 days

  5. 30 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work = 6 men * 19 days = 114 man-days. The new capacity is 4 men + 0.5 men + 0.25 men = 4.75 men. Time = 114 / 4.75 = 24 days.

Multiple choice

Four men or six children can do a piece of work in 12 days, working 7 hours a day. How many days will it take to complete a piece of work thrice as large as the first, with 12 men and 3 children working together 8 hours a day?

  1. 10

  2. 7

  3. 9

  4. 8

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

4 men = 6 children, so 1 man = 1.5 children. 12 men + 3 children = 12(1.5) + 3 = 18 + 3 = 21 children. Work 1: 6 children * 12 days * 7 hours = 504 man-hours. Work 2: 3 * 504 = 1512 man-hours. New group: 21 children * D days * 8 hours = 1512. D = 1512 / 168 = 9.

Multiple choice

4 women and 5 men can complete a certain work in X days, while 4 men and 1 woman can complete the same work in Y days. The work completed by 1 man in 1 day is 250% of the work completed by 1 woman in 1 day. Which of the following is the ratio of the number of days required to complete the work by 4 women and 5 men together and the number of days required to complete the work by 4 men and 1 woman together? (i) 5 : 3 (ii) 2 : 3 (iii) 4 : 3 (iv) 6 : 5

  1. Only (i)

  2. Only (ii)

  3. Only (iii)

  4. Only (iv)

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

Q alone can complete the same job in how many days? (i) The efficiency of R is 25% more than the efficiency of S. (ii) The efficiency of Q is two times more than the efficiency of R. (iii) R and S together can complete the job in 80/3 days. (iv) P and Q together can complete the job in 24 days. Which of the given statements is redundant to find the answer of the question?

  1. Statement (ii)

  2. Statement (iii)

  3. Statement (i)

  4. Statement (iv)

  5. Answer cannot be determined even after using all the statements.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find Q's time, we need Q's efficiency. (i) gives R vs S. (iii) gives R+S efficiency. Together (i) and (iii) give R and S efficiencies. (ii) gives Q in terms of R. Thus (i), (ii), and (iii) are sufficient to find Q's efficiency. Statement (iv) relates P and Q, which is not needed to find Q's individual time.

Multiple choice

(x + 5) men can complete a work in (x - 4) days, while (x + 10) women can complete the same work in (x - 6) days. Work completed by 1 man in 9 hours is the same as the work completed by 1 woman in 8 hours. If 'y' men can complete the same work in 10 days and 'z' women can complete the same work in 4 days, then which of the following values of x, y and z, respectively can satisfy the above given condition. (i) 10, 5, 20 (ii) 10, 6, 20 (iii) 20, 4, 10 (iv) 10, 5, 10

  1. Only (iv)

  2. Only (i)

  3. Only (ii)

  4. Only (iii)

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

13 men can do a work in x days and 17 women can do the same work in (x + 10) days. 13 men and 17 women together can do the same work in (75/8) days. With the assistance of 5 children, they finished the work in 5 days. If they undertook the work for Rs. 15,000, then what is the share of 1 child?

  1. Rs. 1,300

  2. Rs. 1,500

  3. Rs. 1,200

  4. Rs. 1,400

  5. Rs. 1,450
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 1 unit. 13 men = 1/x, 17 women = 1/(x+10). Together 13 men + 17 women = 8/75. 1/x + 1/(x+10) = 8/75. Solving gives x=15. 13 men = 1/15, 17 women = 1/25. Together they do 8/75. In 5 days, they do 8/15. Remaining work = 7/15. 5 children do 7/15 in 5 days, so 7/75 per day. Total wages are proportional to work done. Share of 5 children = (7/15) * 15000 = 7000. Share of 1 child = 1400.

Multiple choice

10 மனிதர்களால் 8 நாட்களில் கட்டிமுடிக்க கூடிய ஒரு கட்டுமான பணியை அரை நாளில் முடிக்க எத்தனை மனிதர்கள் வேண்டும்? 10 men can complete the construction work in 8 days. How many men do you need to complete the same task in half a day?

  1. 80

  2. 100

  3. 120

  4. 160

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

This is an inverse proportion problem. M1 * D1 = M2 * D2. 10 * 8 = M2 * 0.5. 80 = 0.5 * M2. M2 = 160.