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, B and C can individually complete a work in 10, 20 and 30 days respectively. If they work on alternate days starting with C then B and A (i.e., Day1: C, Day2: B, Day3: A, Day4: C, ...), in how many days will the work be completed?

  1. 17 days

  2. 18 days

  3. 16 days

  4. 15 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work rates: A=1/10, B=1/20, C=1/30. Cycle (C, B, A): 1/30 + 1/20 + 1/10 = (2+3+6)/60 = 11/60. In 15 days (5 cycles), work done = 5 * 11/60 = 55/60. Remaining = 5/60 = 1/12. Day 16 (C): 1/30 done. Day 17 (B): 1/20 done. Total work is completed on day 17.

Multiple choice

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs. 2,160, Rs. 2,400, and Rs. 2,160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

  1. 34,400

  2. 38,400

  3. 47,040

  4. 38,880
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To minimize cost, use the most efficient workers. Arun (1/24), Varun (1/21), Tarun (1/15). Tarun is fastest. To finish in 10 days, we need total work = 1. Tarun does 10/15 = 2/3. Remaining 1/3 work can be done by Varun in (1/3)*21 = 7 days. Total cost = 10*2160 + 7*2400 = 21600 + 16800 = 38400.

Multiple choice

Arjun and Meera together can complete a certain assignment in 36 days. On a day when Arjun works at only 60% of his usual capacity, Meera needs to work at 160% of her normal rate to keep their combined daily output unchanged. How many days would the quicker of the two take to finish the assignment working alone?

  1. 30

  2. 45

  3. 60

  4. 75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and M be rates. (A+M)*36 = 1. (0.6A + 1.6M)*36 = 1. So A+M = 0.6A + 1.6M => 0.4A = 0.6M => A = 1.5M. Substitute into A+M = 1/36: 2.5M = 1/36 => M = 1/(36*2.5) = 1/90. A = 1.5/90 = 1/60. The quicker one is A, taking 60 days.

Multiple choice

Sonia, Arjun, and Priya, working together, would have taken at least 10 days to complete a project. Sonia and Priya, working together, would have taken less than 25 days to complete the same project. In reality, all three worked together for 8 days, followed by Arjun, who worked alone for 4 more days to finish the project. If Arjun had worked alone on the project, then the number of days he would have taken to complete it cannot be

  1. 17

  2. 18

  3. 19

  4. 20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let S, A, P be the work rates. (S+A+P) >= 1/10. (S+P) < 1/25. 8(S+A+P) + 4A = 1. If Arjun takes T days, A = 1/T. 8(S+P+1/T) + 4/T = 1 => 8(S+P) + 12/T = 1. Since S+P < 1/25, 8(S+P) < 8/25 = 0.32. So 1 - 12/T < 0.32 => 12/T > 0.68 => T < 17.64. Also (S+A+P) >= 1/10 => 1/T + (S+P) >= 1/10. Since S+P < 1/25, 1/T > 1/10 - 1/25 = 3/50 = 0.06 => T < 16.66. The value 17 is not possible.

Multiple choice

Three technicians—Arun, Bala, and Charan—can complete a machine-assembly job on their own in 12, 18, and 36 days, respectively. Their daily wages are Rs. 900, Rs. 600, and Rs. 400, respectively. If all three work together from the start and are paid their respective daily wages for each day they work, what is the total amount (in Rs.) paid to complete the job?

  1. 11,100

  2. 11,400

  3. 14,100

  4. 14,400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work rates: A=1/12, B=1/18, C=1/36. Combined rate = (3+2+1)/36 = 6/36 = 1/6. Job takes 6 days. Total wages = 6 * (900 + 600 + 400) = 6 * 1900 = 11400.

Multiple choice

Veer can complete a renovation project in 2x + 5 days, while Simran can do it in x days and Kabir in 2x days. Veer works alone for 3 days, after which Simran, Kabir, and Diya join him, and together they complete the remaining work in 4 more days. If the total payment for the project is Rs. 32,000 and Diya's share is 12% of the total payment, then in how many days can Simran complete the renovation work alone?

  1. 8

  2. 9

  3. 10

  4. 12

  5. 15
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

A can finish a work in 15 days, B can finish the same work in 25 days. They work together for 5 days. The rest of the work is finished by A and C in 4 days. Then C alone can finish the work in ?

  1. 18 days

  2. 24 days

  3. 20 days

  4. 21 days

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

A's rate = 1/15, B's rate = 1/25. Combined = 8/75. In 5 days, they do 40/75 = 8/15. Remaining = 7/15. A and C do this in 4 days, so (1/15 + C) * 4 = 7/15 => 1/15 + C = 7/60 => C = 3/60 = 1/20. C takes 20 days.

Multiple choice

Jassi , Pammi and Mani can do a piece of work individually in 8 , 12 and 4 days respectively. Jassi started the piece of work and is assisted by Pammi and Mani on every third day. Then in how many days will the work be completed ?

  1. 4(1/2)

  2. 4(2/3)

  3. 5(1/11)

  4. 5(1/9)

  5. 7(1/9)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the total work be 24 units. The daily work rates for Jassi, Pammi, and Mani are 3, 2, and 6 units respectively. In a 3-day cycle, Jassi works alone for 2 days (6 units) and all three work together on the third day (11 units), totaling 17 units. On days 4 and 5, Jassi adds 6 units, leaving 1 unit which is completed by all three together in 1/11 of day 6, totaling 5(1/11) days.