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

Jacob, Jack, Summer and Amina are doing same work. Jack takes 4 days more than Jacob. The efficiency of Jack is double that of Summer. The ratio of efficiencies of Summer and Amina is 1 : 4. Amina takes 8 days to complete the work. A. Jacob takes 12 days to complete the work. B. The difference between the number of days taken by Jack and by Summer to complete the work alone is 20. C. Jack takes the least number of days to complete the work. D. Jacob and Jack will take 8 days to complete the work together. Which of the above statements is/are correct?

  1. (A), (B) and (D)

  2. (A) and (C) only

  3. (A) and (B) only

  4. (A) only

  5. NA
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Amina takes 8 days. Efficiency ratio Summer:Amina = 1:4. Summer takes 4 times longer = 32 days. Efficiency Jack = 2 * Summer = 2 * (1/32) = 1/16. Jack takes 16 days. Jack takes 4 days more than Jacob, so Jacob takes 12 days. (A) Jacob takes 12 days is correct. (B) Jack (16) - Summer (32) = 16, not 20. (C) Jack (16) vs Jacob (12), Jacob is faster. (D) 1/12 + 1/16 = 7/48. Time = 48/7 = 6.85 days.

Multiple choice

A can complete a piece of work in 9 days, while B can complete the same work in 12 days. A and B charged Rs. 5,400 to complete the work. With the help of C, they all completed the work in 4 days. Statement I: C can complete the work alone in 18 days. Statement II: C's share in the completed work is Rs. 800. In the light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.

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

A's rate = 1/9, B's rate = 1/12. (A+B+C) rate = 1/4. C's rate = 1/4 - 1/9 - 1/12 = (9-4-3)/36 = 2/36 = 1/18. So C completes work in 18 days (Statement I is true). C's share = (1/18) * 5400 = 300 (Statement II is false).

Multiple choice

A group of workers A, B, C and D is assigned to complete a construction project. They have varying efficiencies, and the time taken by each of them individually to complete the project is given as follows: A takes twice as long as B, B takes three times as long as C, and C takes four times as long as D. Together, they complete 1/4th of the project in 5 days, working 8 hours per day. However, due to unforeseen circumstances, workers A and D are unable to continue working on the project. The remaining work is done by workers B and C. If B and C work only 6 hours a day, find the number days required to finish the remaining project by workers B and C.

  1. 27.5 days

  2. 38 days

  3. 82.5 days

  4. 110 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

A construction project requires the collaboration of three teams, A, B, and C to complete the task. Each team has a different number of workers. Team A consists of 10 skilled workers, each capable of completing a task in 5 days. Team B consists of 15 apprentices, and each apprentice takes 8 days to complete same task. Team C comprises 5 experienced workers who can finish same task in 3 days. However, due to unforeseen circumstances, Team C is only available to work for the first 6 days. If the construction project requires 45 times of task to be completed, and each team maintains a consistent efficiency throughout the project, how many additional days will it take for Teams A and B to finish the remaining tasks after the first 6 days?

  1. 3 days

  2. 3 1 31 d a y s

  3. 6 days

  4. 6 1 31 d a y s

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

In an office setup, there are four departments: Department A, Department B, Department C, and Department D. If four employees from Department A, six employees from Department B and eight employees from Department C work together, they can complete a project in 5 days. However, if five employees from Department A, 10 employees from Department C and five employees from Department D work together, they can finish the same project in 4 days. Alternatively, if three employees from Department B and six employees from Department D work together, they can complete the same project in 8 days. Given these scenarios, how many employees from Department D can complete the same project in one day?

  1. 68

  2. 64

  3. 56

  4. 46

  5. 42
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Directions: The problem contains a question and two statements giving certain data. You have to select the correct answer from the given options depending on the sufficiency of the data given in the statements to answer the question. How many workers are required to complete a project in 10 days? (A) 20 workers can complete the project in 15 days. (B) 60 workers can complete the project in 5 days.

  1. Statement (A) alone is sufficient, but statement (B) alone is not sufficient.

  2. Statement (B) alone is sufficient, but statement (A) alone is not sufficient.

  3. Both (A) and (B) together are sufficient, but none of them alone is sufficient.

  4. Both the statements are sufficient independently.

  5. Both (A) and (B) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A: 20 workers * 15 days = 300 man-days. To find workers for 10 days, 300/10 = 30 workers. Statement B: 60 workers * 5 days = 300 man-days. To find workers for 10 days, 300/10 = 30 workers. Both statements independently provide the total work required.

Multiple choice

Directions: In the following item, Quantity I and Quantity II are given. Determine the relationship between the quantities and choose the appropriate option. Three workers, A, B, and C, can complete a task in 12, 15, and 20 days, respectively, working alone. Quantity I: The total number of days it would take for workers A and B to complete the task if they work together Quantity II: The number of days it would take for workers B and C to complete the entire task if they work together

  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 No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: A and B together = 1 / (1/12 + 1/15) = 1 / (9/60) = 60/9 = 6.67 days. Quantity II: B and C together = 1 / (1/15 + 1/20) = 1 / (7/60) = 60/7 = 8.57 days. Since 6.67 < 8.57, Quantity I < Quantity II.

Multiple choice

Given below are two statements: Statement I: Ram and Shyam can finish a task by working together in 6 days. If Shyam can finish the task by working alone in 8 days, then Ram alone will take 24 days to finish it. Statement II: If 6 persons working 8 hours a day earn ₹8,400 per week, then 9 persons working 6 hours a day will earn ₹9,450 per week. In the light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement I is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: 1/R + 1/8 = 1/6, so 1/R = 1/6 - 1/8 = 1/24, R = 24. True. Statement II: (6*8)/8400 = (9*6)/X, so 48/8400 = 54/X, X = 54 * 8400 / 48 = 9450. True.

Multiple choice

Directions: The question below consists of a question and two statements, labeled (1) and (2), in which certain data is given. Decide whether the data given in the statements is sufficient for answering the question. Using the data provided in the statements and knowledge of mathematics and everyday facts, mark the following: If Andy and Sandy, working together, can paint a house in 5 days, can Andy paint the same house in 8 days? 1. Andy is faster than Sandy. 2. Sandy can paint the same house in 10 days.

  1. If statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question

  2. If statement (2) alone is sufficient, but statement (1) alone is not sufficient to answer the question

  3. If both statements (1) and (2) together are sufficient to answer the question, but neither statement alone is sufficient

  4. If each statement alone is sufficient to answer the question

  5. If statements (1) and (2) together are not sufficient to answer the question and an additional data, that is specific to the problem, is needed
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A and S be the rates of Andy and Sandy. 1/A + 1/S = 1/5. Statement 2 says S = 1/10. Substituting this: 1/A + 1/10 = 1/5 => 1/A = 1/10 => A = 10. So Andy takes 10 days, not 8. Statement 2 is sufficient to answer the question (the answer is no). Statement 1 is not sufficient as it only gives a relative comparison.

Multiple choice

A warehouse is tasked with sorting 1,560 packages per day. Male and female workers are employed for this job, with each worker working 8 hours per day. A male worker can sort 25 packages per hour, and a female worker can sort 30 packages per hour. Male workers receive a fixed wage of Rs. 300 per day and Rs. 12 per package sorted, while female workers receive a fixed wage of Rs. 350 per day and Rs. 10 per package sorted. How many male workers should the warehouse employ, given that it must employ at least 3 and at most 7 female workers, and what will be the total operational cost per day with the given condition?

  1. 2, Rs. 20,100 per day

  2. 3, Rs. 19,100 per day

  3. 4, Rs. 15,400 per day

  4. 5, Rs. 19,200 per day

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

Total packages = 1560. Let M be male workers and F be female workers. Total sorted = 25*8*M + 30*8*F = 200M + 240F = 1560. Simplifying, 5M + 6F = 39. Given 3 <= F <= 7, testing values: if F=4, 5M = 39-24=15, M=3. If F=3, 5M=21 (no). If F=7, 5M= -3 (no). With M=3, F=4: Cost = (300+12*25*8)*3 + (350+10*30*8)*4 = (300+2400)*3 + (350+2400)*4 = 2700*3 + 2750*4 = 8100 + 11000 = 19100.

Multiple choice

Directions: The following problem consists of a question and two statements labelled (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question. What is the daily average wage of a worker if he works for five days and if he made Rs. 80 on the first day? I. The worker made a total of Rs. 400 during the first four days. II. The worker made Rs. 20 more each day than he did on the previous day. Mark your answer as

  1. if statement I alone is sufficient to answer the question

  2. if statement II alone is sufficient to answer the question

  3. if both statements I and II together are necessary to answer the question

  4. if both statements I and II together are not sufficient to answer the question

  5. if either statement I alone or statement II alone is sufficient to answer the question
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The question asks for the average wage over 5 days. Statement II says the worker made 20 more each day than the previous day. With day 1 = 80, the sequence is 80, 100, 120, 140, 160. This is sufficient to find the average.

Multiple choice

Directions: The following problem consists of a question and two statements numbers I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read the both the statements and mark your answer accordingly. Three employees A, B and C are working on an assignment. In how many days can they finish this assignment? Statement I: The time taken by employee A alone to complete the assignment is 24 days less than the time taken by employee C alone to finish the same assignment. Statement II: Employees A and B together can finish the assignment in 6 days. Employees B and C together can finish the assignment in 12 days. Employees C and A together can finish the assignment in 10 days.

  1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in both statements I and II together is necessary to answer the question.

  4. The data in statement I alone or in statement II alone is sufficient to answer the question.

  5. The data in both statements I and II is not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II provides a system of equations: A+B=1/6, B+C=1/12, C+A=1/10. This is sufficient to solve for A, B, and C individually, and thus their combined rate. Statement I is insufficient on its own.

Multiple choice

Directions: Question given below contains a statement followed by Quantity I and Quantity II. Find the relationship between them and choose the answer accordingly. A man can do a piece of work in 20 days. The efficiency of a woman is 100% more than that of the man. On each day, one man and two women together make 120 chairs. They do the same work everyday. Quantity I: If three men and one woman did the work each day, then in how many days would the work be finished? Quantity II: If five women work on each day, then in how many days would the work be finished?

  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 relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Man efficiency = 1 unit/day. Woman efficiency = 100% more = 2 units/day. 1 man + 2 women = 1 + 2(2) = 5 units/day. Total work = 120 chairs/day * 20 days = 2400 chairs. Quantity I: 3 men + 1 woman = 3(1) + 2 = 5 units/day. Days = 2400 / 5 = 480 days. Quantity II: 5 women = 5(2) = 10 units/day. Days = 2400 / 10 = 240 days. Quantity I > Quantity II.

Multiple choice

Four people – A, B, C and D, started working on a project. It is known that, B is two-third as efficient as C, half as efficient as C and 50% more efficient than D. Each day, one of them takes a day-off. On Day 1, only A, B and C work together. On Day 2, only A, B and D work together. On Day 3, only B, C and D work together. On Day 4, only A, C and D work together. They repeat this four-day schedule until the project is completed. Had the project been completed by only C and D, working together every day, they would have taken 72 days to complete it. Among the total number of days they took to complete the project, how many days did C work?

  1. 11

  2. 12

  3. 36

  4. 37
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Directions: The question below is followed by two statements A and B. You are to determine whether the data given in the statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose between the possible answer. How many women can complete a piece of work in 10 days? A. If the same piece of work is completed by 4 men in 6 days. B. If the same piece of work is completed by 7 women in 14 days.

  1. if the statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.

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

  3. if both statements A and B together are needed to answer the question.

  4. if either the statement A alone or statement B alone is sufficient to answer the question.

  5. if you cannot get the answer from the statement A and B together, but need even more data.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The question asks for the number of women required to complete a work in 10 days. Statement B provides the rate of work for women (7 women in 14 days), which allows calculating the total work and thus the number of women needed for 10 days. Statement A relates men to the work but does not provide the conversion factor between men and women, so it is insufficient on its own.