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

Directions: The following item contains two statements, I and II, giving certain data. Select the correct answer from (1) to (4) depending on the sufficiency of the data given in the statements to answer the question. P and Q started working on an assignment together. But due to some heath problems, after 3 days, Q had to leave the assignment, and P alone completed the remaining assignment. In how many days was the whole assignment completed? Statement I: P alone can complete the whole assignment in 21 days. Statement II: Q alone can complete the whole assignment in 14 days.

  1. I alone is sufficient but II alone is not sufficient to answer the question.

  2. II alone is sufficient but I alone is not sufficient to answer the question.

  3. Both I and II together are sufficient but neither statement alone is sufficient to answer the question.

  4. Both I and II together are not sufficient to answer the question, and additional data, specific to the question, is needed.

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

Statement I gives P's rate as 1/21 of the assignment per day, while statement II gives Q's rate as 1/14 per day. Both rates are needed to determine the work completed together during the first 3 days and the remaining time taken by P. Therefore, both statements together are sufficient, but neither alone is sufficient.

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. In how many days A will complete the work, if B takes 10 more days than A and C takes 4 less days than B to do the same work. (A) Time taken by B & C together is 10/9 less days than that by A alone. (B) A & C together will take less time than the taken by B & C together

  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
A Correct answer
Explanation

Let A's time be x. B's time is x + 10. C's time is (x + 10) - 4 = x + 6. Statement A provides the relationship between the combined work rate of B and C and A's work rate, which is sufficient to solve for x. Statement B is a qualitative comparison and does not provide enough numerical data to solve for x.

Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. X can complete a job in 10 days and X, Y and Z together can complete the same job in 5 days. Y can complete the same job in how many day? (1) Z can complete the same job in 30 days. (2) Y is 2 time efficient than Z.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R_x, R_y, R_z be the rates. We know R_x = 1/10 and R_x + R_y + R_z = 1/5. Thus, R_y + R_z = 1/10. Statement (1) gives R_z = 1/30, allowing us to find R_y. Statement (2) gives R_y = 2 * R_z, which combined with R_y + R_z = 1/10 also allows us to find R_y. Both statements are sufficient independently.

Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. Find the number of days in which Rahim can complete a piece of work. (1) Rahim and Sunil together can complete the same piece in 72/7 days. (2) Rahim is 33.33% more efficient than Sunil.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Both the statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement (1) gives the combined rate of work. Statement (2) provides the ratio of their efficiencies. To find the individual time, you need both the combined rate and the relative efficiency to set up a system of equations.

Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. P, Q and R can complete 1/3rd of the total work in 28/9 days and P alone can complete the whole work in 42 days. In how many days can Q alone complete 1/2 of the total work? (1) The efficiency of Q is 4/3 times of the efficiency of R. (2) R can complete the whole work in 28 days.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statementd (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Together, P, Q, and R work at 3/28 of the task per day, while P works at 1/42, so Q + R work at 1/12 per day. Statement 1 gives Q = 4R/3, which determines Q, and statement 2 directly gives R = 1/28, which also determines Q. Each statement alone is sufficient.

Multiple choice

Directions: The following question is accompanied by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the question. If 23 unskilled and 20 skilled persons together can complete a project in 12 days, then 20 unskilled persons alone can complete the same project in how many days? (A) The skilled persons are 30% more efficient than the unskilled persons. (B) 25 unskilled and 26 skilled persons together can complete the same project in 10 days.

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

  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 question, 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

Let U be the efficiency of an unskilled person and S be the efficiency of a skilled person. Statement A gives S = 1.3U. Statement B gives a second equation for the same project. Both statements allow solving for the efficiency ratio and the total work, making either sufficient.

Multiple choice

Directions: The following question is accompanied by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the question. (X + 10) persons can complete the project p1 in how many day? (A) X person can complete 40% of the project p1 in 15 days and remaining work is completed by (X + 25) persons in 10 days. (B) The ratio of work of project p1 done by X person to that of (X + 25) persons is 4 : 9

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

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

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

  4. Both the statements taken together are necessary to answer the questions, but neither of the statements alone 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
A Correct answer
Explanation

Statement A provides enough information to calculate the work rate of X and (X+25), allowing us to solve for X and then the total time for (X+10) persons. Statement B only provides a ratio, which is insufficient without total work or time.

Multiple choice

In the given questions, two quantities are given, one as Quantity I and another as Quantity II. You have to determine relationship between two quantities and choose the appropriate option. B is thrice as efficient as C. B and C can compete a work together in 45/2 days. A takes 50% more days than the days taken by A and B to complete the same work together. Quantity 1: No. of days taken by fastest among them to complete the work alone. Quantity 2: Time taken by A and C to complete the 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
A Correct answer
Multiple choice

X, Y, and Z are three software experts, who work on upgrading the software in a number of identical systems. X takes an off after every 3 days of work, Y takes an off after every 4 days of work and Z takes an off after every 5 days of work. Starting afresh after a common day off: (i) X and Y working together can complete one new upgrade job in 6 days (ii) Z and X working together can complete two new upgrade jobs in 8 days (iii) Y and Z working together can complete three new upgrade jobs in 12 days If X, Y and Z together start afresh on a new upgrade job (after a common day off), exactly how many days will be required to complete this job?

  1. 2 days

  2. 3.5 days

  3. 2.5 days

  4. 4 days

  5. 3 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: Two friends A and B together can complete a piece of work in 10 days. In how many days A alone complete the piece of work? Statement I : B alone can complete half of the work in 12.5 days. Statement II : The efficiency of A is 50% more than that of B.

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

  3. Either Statement I or Statement II alone is sufficient to answer the question.

  4. Neither statement I nor statement II is sufficient to answer the questions.

  5. The data in both the statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B = 1/10. Statement I: B = 1/25, so A = 1/10 - 1/25 = 3/50 (A takes 16.6 days). Statement II: A = 1.5B, so 1.5B + B = 1/10, 2.5B = 1/10, B = 1/25, A = 3/50. Both are sufficient alone.

Multiple choice

Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: There are three people A, B and C. Find the time taken by C to complete the whole work. Statement I : A and B together can complete the work in 16 days while B and C can complete the whole work in 20 days. Statement II : A and B together can complete the work in 16 days. Efficiency of A and B is same.

  1. If 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. If 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. If the data either in statement I alone or in statement II alone is sufficient to answer the question

  4. If the data in both statements I and II together are necessary to answer the question

  5. If the data given in both statements I and II together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: 1/(A+B) = 1/16, 1/(B+C) = 1/20. We have two equations with three variables (A, B, C), so we cannot find C alone. Statement II: A=B, 1/(A+B) = 1/16. This gives A and B, but no information about C. Combining both: A=B=8 days, then 1/8 + 1/C = 1/20. This allows solving for C.

Multiple choice

Directions: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You are to use the given data and your knowledge of Mathematics to choose among the given options. Quantity I: Anjali can complete a task in 50 days and Pallavi is 30% more efficient than her. Number of days taken by Pallavi to finish the task Quantity II: A task is completed by 18 girls and 24 boys in 12 days. Number of days taken by 6 girls and 8 boys to complete the task

  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
A Correct answer
Explanation

Quantity I: Anjali = 50 days. Pallavi is 30% more efficient, so she takes 50/1.3 = 38.46 days. Quantity II: 18 girls + 24 boys = 12 days. 6 girls + 8 boys is exactly 1/3 of the workforce, so they take 12 * 3 = 36 days. Since 38.46 > 36, Quantity I > Quantity II.

Multiple choice

Given: Anuj takes 1 day to complete a job. Bharat takes twice the time as Anuj to complete the same job. Chetan takes twice the time as Bharat to complete that job. Dhiraj takes twice the time as Chetan to complete that job. (A) Chetan and Dhiraj will take 8/3 days to complete the work. (B) The second fastest pair to complete the work is Anuj and Dhiraj. (C) The second slowest pair to complete the work is Bharat and Dhiraj. (D) Bharat and Dhiraj will take 4/3 days to complete the work. Choose the correct answer from the options given below:

  1. (A), (B) and (C) only

  2. (A) and (D) only

  3. (A) and (C) only

  4. (A) only
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Directions: In the following question, a given questions is followed by information in three statements. You have to decide the data in which statement (s) is sufficient to answer the question and mark your answer accordingly. How many days A, B and C can complete the work together? Statement I - Ratio of efficiency of A and B is 2:1. Band C can complete the work in 12 days. Statement II - Ratio of efficiency of A and C is 3:1. C can alone complete the work in 30 days.

  1. Only Statement I alone.

  2. Only Statement II alone.

  3. Both Statements I and II together.

  4. Neither Statement I nor II is sufficient.

  5. Either Statement I or II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I: A:B = 2:1, B+C = 12 days. Statement II: A:C = 3:1, C = 30 days. From II, C=30, A=10. From I, B=15. With A, B, and C efficiencies known, we can calculate the time taken to complete the work together.

Multiple choice

Each of the questions 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: Rani, Supriya and Amita work on a project. If each of them is of a different efficiency. Who is the fastest worker among them? Statement I : Rani and Supriya take 5 days to complete the project while Supriya and Amita take 10 days to complete the same project. Statement II : Rani and Amita take 30/7 days to complete the project.

  1. If 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. If 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. If the data either in statement I alone or in statement II alone is sufficient to answer the question

  4. If the data in both statements I and II together are necessary to answer the question

  5. If the data given in both statements I and II together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
A Correct answer