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

Thomas can paint the house in $6$ days while it takes Joe $12$ days to paint the same house. How long would it take Thomas and Joe, working together, to paint the house?
  1. $3$ days
  2. $4$ days
  3. $5$ days 
  4. $6$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Thomas paints 1/6 of the house per day, and Joe paints 1/12 of the house per day. Together, their combined rate is 1/6 + 1/12 = 3/12 = 1/4 of the house per day. Therefore, it takes them 4 days to complete the entire house.

Multiple choice

Raman can do a work in $5$ days, Jatin can do the same work in $7$ days and Sachin can do the same work in $9$ days. If they do the same work together and they are paid Rs. $2860$, then what is the share (in Rs.) of Raman?
  1. $1260$
  2. $700$
  3. $900$
  4. $870$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work shares are proportional to efficiency (1/time). Efficiencies: Raman = 1/5, Jatin = 1/7, Sachin = 1/9. Ratio = 63:45:35. Total parts = 143. Raman's share = (63/143) * 2860 = 63 * 20 = 1260.

Multiple choice

This data sufficiency problem consists of a question and two statements labelled (1) and (2), which contain certain data. Using these data and your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), decide whether the data given are sufficient for answering the question and then indicate one of the following answer choices: Mary and Nancy can each perform a certain task in $m$ and $n$ hours, respectively. Is $m < n$? (1) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is greater than m. (2) Twice the time it would take both Mary and Nancy to perform the task together, each working at their respective constant rates, is less than n

  1. Data in statement I alone is sufficient.

  2. Data in statement II alone is sufficient.

  3. Data in both statements together is sufficient.

  4. Either of the Statements I and II is sufficient

  5. Data in both statements together is not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let T = mn/(m+n) be the time taken together. (1) 2T > m implies 2n/(m+n) > 1, so 2n > m+n, n > m. (2) 2T < n implies 2m/(m+n) < 1, so 2m < m+n, m < n. Both statements independently prove m < n.

Multiple choice

Widgets Hours Breaks Rishi 28 4 2 Dillyn 42 6 4 Shane 27 5 2 Rishi, Shane, and Dillyn work at a widget factory. The table above shows the number of hours they each spent at the factory on a given day, the number of widgets they produced, and the number of 15-minute breaks they took while they were at the factory. Each man works at a constant rate. Rishi and Shane are each assigned an equal number of widgets. Neither will take breaks in order to complete this assignment as quickly as possible. I order that they both finish the assignment at the same time , Rishi offers to do a certain percentage of Shane's assignment. What percentage of Shane's original assignment does Rishi do?
  1. $12.5\%$
  2. $14.3\%$
  3. $16.7\%$
  4. $25\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rishi's rate is 28/4 = 7 widgets/hr. Shane's rate is 27/5 = 5.4 widgets/hr. To finish the same number of widgets (let this be W) at the same time, they must work for the same duration. If they work for time T, 7T + 5.4T = 2W. Solving for T in terms of W, then finding how much of Shane's work Rishi covers, leads to the percentage.

Multiple choice

$2$ women and $5$ men can together finish an embroidery work in $4$ days, while $3$ women and $6$ men can finish it in $3$ days. Find the time taken by $1$ woman as well as $1$ man to finish the work if each of them works alone.
  1. Time taken by $1$ woman alone to finish the work: $24$ days, and also that taken by $1$ man alone: $32$ days
  2. Time taken by $1$ woman alone to finish the work: $18$ days, and also that taken by $1$ man alone: $36$ days
  3. Time taken by $1$ woman alone to finish the work: $14$ days, and also that taken by $1$ man alone: $30$ days
  4. Time taken by $1$ woman alone to finish the work: $12$ days, and also that taken by $1$ man alone: $28$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let W be the work of a woman and M be the work of a man per day. 2W + 5M = 1/4 and 3W + 6M = 1/3. Solving this system of linear equations yields W = 1/18 and M = 1/36. Thus, a woman takes 18 days and a man takes 36 days.

Multiple choice

$2$ men and $3$ boys together can do a piece of work in $8$ days. The same work is done in $6$ days by $3$ men and $2$ boys together. How long would $1$ boy alone or $1$ man alone take to complete the work.
  1. One boy alone can do a piece of work in $130$ days

    and one man alone can do a piece of work in $160$ days
  2. One boy alone can do a piece of work in $90$ days

    and one man alone can do a piece of work in $70$ days
  3. One boy alone can do a piece of work in $120$ days

    and one man alone can do a piece of work in $20$ days
  4. One boy alone can do a piece of work in $160$ days

    and one man alone can do a piece of work in $12$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M and B be the daily work of a man and a boy. 8(2M + 3B) = 1 => 16M + 24B = 1. 6(3M + 2B) = 1 => 18M + 12B = 1. Solving the system: multiply second by 2: 36M + 24B = 2. Subtracting first: 20M = 1 => M = 1/20. Then 12B = 1 - 18(1/20) = 1 - 0.9 = 0.1 => B = 1/120. Man takes 20 days, boy takes 120 days.

Multiple choice

John alone could complete a given task in 20 days. Jane would take only 12 days to complete the same task alone. John and Jane set out to complete the task by beginning to work together. However, Jane left 4 days before the work was completed. In how many days was the work completed from the time John and Jane started to work on it together?

  1. 6

  2. 10

  3. 8

  4. 7.5

  5. 3.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

John's rate is 1/20, Jane's is 1/12. Let T be total time. John works for T days, Jane for T-4 days. (T/20) + (T-4)/12 = 1. Multiply by 60: 3T + 5(T-4) = 60. 3T + 5T - 20 = 60, 8T = 80, T = 10.

Multiple choice

A, B and C can do a piece of work in 20, 30 and 40 days, respectively. They earn $5,200 for completing the work.Quantity A Difference between A's money and B's money Quantity B Difference between B's money and C's money

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Their work rates are proportional to 1/20, 1/30, and 1/40, or 6:4:3. Their earnings follow this ratio, so the difference between A's and B's earnings is twice the difference between B's and C's earnings.

Multiple choice

Directions: Compare the two quantities in A and B. A is 50% less efficient than B. B takes 12 days to complete a piece of work. Quantity A Quantity B Number of days required for both A and B together to complete the work. 7

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

B's efficiency = 1 unit/day. A's efficiency = 0.5 units/day. Together = 1.5 units/day. Days to complete = 12/1.5 = 8 days. Quantity A (8) > Quantity B (7).

Multiple choice

A woman can do only half of the work that a man can do. 10 men can finish a piece of work in 12 days, working 8 hours per day.Quantity ANumber of days required for 5 men and 5 women to do the same work, working 10 hours a day.Quantity B13

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If one man completes one unit of work, one woman completes half a unit. Thus, 5 men and 5 women equal 7.5 men. The required time is (10 x 12 x 8) / (7.5 x 10) = 12.8 days, which is less than 13 days.

Multiple choice

Directions: Compare the two quantities in A and B. A, B and C can complete a work in 20, 24 and 30 days respectively. Quantity A Quantity B The time required to complete the work if A, B and C work together. The time required by B alone to complete one third of the work.

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity A: 1/20 + 1/24 + 1/30 = (6+5+4)/120 = 15/120 = 1/8. Time = 8 days. Quantity B: B takes 24 days for the whole work, so 1/3 of the work takes 24/3 = 8 days. Both are 8 days.