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 given question is followed by three statements I, II and III. You have to determine which of the statements is/are necessary/sufficient to answer the question. What is the time taken by P, Q and R together to complete the work if R completes the work in 30 days? I. P is 50% more efficient than R. II. Q is 50% more efficient than P. III. P can complete the work in 20 days.

  1. Only statements I and II are sufficient.

  2. Only statements II and III are sufficient.

  3. Only statement II is sufficient.

  4. Only statement II and either I or III are sufficient.

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

R takes 30 days. P is 50% more efficient than R, so P's time = 30 / 1.5 = 20 days. Q is 50% more efficient than P, so Q's time = 20 / 1.5 = 40/3 days. Statement II provides Q's efficiency relative to P, and either I or III allows finding P's efficiency relative to R or directly. Thus, II and (I or III) are sufficient.

Multiple choice

A is 40% less efficient than B who can do the same work in 20% less time than C. If A and B together can complete 80% work in 12 days, then in how many days 60% work can be completed by B and C together?

  1. 2 days

  2. 4 days

  3. 8 days

  4. 16 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Efficiency A = 0.6 * Efficiency B. Time B = 0.8 * Time C, so Efficiency B = 1/0.8 * Efficiency C = 1.25 * Efficiency C. A+B complete 80% in 12 days, so 100% in 15 days. (Eff A + Eff B) = 1/15. 0.6B + B = 1/15 -> 1.6B = 1/15 -> B = 1/24. C = B/1.25 = 1/30. B+C efficiency = 1/24 + 1/30 = (5+4)/120 = 9/120 = 3/40. Time for 60% work = 0.6 / (3/40) = 0.6 * 40 / 3 = 8 days.

Multiple choice

A can complete a piece of work in 20 days and B can do the same in 30 days. They work together for 8 days and then A leaves the work. How many days will B take if he has to complete the pending work alone?

  1. 10 days

  2. 20 days

  3. 40 days

  4. 60 days

  5. 90 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate = 1/20, B's rate = 1/30. Combined rate = 1/20 + 1/30 = 5/60 = 1/12. In 8 days, they finish 8/12 = 2/3 of the work. Remaining work = 1/3. B takes (1/3) / (1/30) = 10 days.

Multiple choice

A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by ________ each working now for 10 hours daily, the work can be completed in time.

  1. 150 men

  2. 200 men

  3. 250 men

  4. 300 men
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work done = 75 * 90 * 8 = 54000 man-hours for 2/7 of work. Total work = 54000 * 3.5 = 189000. Remaining work = 5/7 = 135000. Time remaining = 60 days. Men needed = 135000 / (60 * 10) = 225. Additional men = 225 - 75 = 150.

Multiple choice

John and Emma are working on a landscaping project for their community park. John can complete 50% of the project in 10 days, while Emma can finish 75% of the project in 15 days. They both work together for 8 days before taking a break. Sarah, a skilled landscaper, then completes the remaining work in 5 days. The community project committee wants to know in how many days it would take John, Emma, and Sarah to collectively finish 35% of similar project if they worked together from the start?

  1. 1.5 days

  2. 2.5 days

  3. 3 days

  4. 4.5 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

John rate: 0.5/10 = 0.05/day. Emma rate: 0.75/15 = 0.05/day. Combined rate = 0.1/day. In 8 days, they finish 0.8 of the project. Remaining = 0.2. Sarah does 0.2 in 5 days, so Sarah rate = 0.04/day. Combined rate of all three = 0.05 + 0.05 + 0.04 = 0.14/day. Time to finish 0.35 of the project = 0.35 / 0.14 = 2.5 days.