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 and B can do a piece of work in 30 days and 40 days respectively after 3 days start of work A leave the job in how many days B can do the remaining of work alone.

  1. 33 days

  2. 26 days

  3. 13 days

  4. 30 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's work rate is 1/30 per day. B's work rate is 1/40 per day. In 3 days together, they complete 3(1/30 + 1/40) = 3(7/120) = 7/40 of the work. Remaining work is 1 - 7/40 = 33/40. B alone needs (33/40) ÷ (1/40) = 33 days to finish the remaining work. Option A is correct.

Multiple choice

20 boys do one fourth of work in 25 days. How many more boys will be required to complete the remaining work in 50 days?

  1. 8

  2. 10

  3. 15

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

20 boys complete 1/4 of the work in 25 days, so the work rate is (1/4) / (20 × 25) = 1/2000 per boy-day. The remaining 3/4 of the work must be completed in 50 days. Let x be the additional boys needed: (20 + x) × 50 × (1/2000) = 3/4. Solving gives 20 + x = 30, so x = 10 more boys are required.

Multiple choice

A and B can do a piece of work in 40 days. They work together for 8 days and then A quits and B finishes the work in 36 more days. In how many days can B do the piece of work alone?

  1. 45

  2. 52

  3. 60

  4. 36
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Combined rate of A and B is 1/40 work per day. In 8 days, they complete 8/40 = 1/5 of work, leaving 4/5. B finishes this 4/5 in 36 days, so B's rate is (4/5)/36 = 1/45 per day. Therefore, B alone can complete the work in 45 days. The other options don't satisfy the work equation.

Multiple choice

A is 1.5 times efficient than B therefore takes 8 days less than B to complete a work. If A and B work on alternate days and A works on first day, then in how many days the work will be completed?

  1. 17

  2. 19

  3. 18

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

A is 1.5 times efficient as B, so A's work: B's work = 3:2. Let A take x days, B takes x+8 days. Work ratio gives (x+8)/x = 3/2, so 2x+16 = 3x, x = 16. A takes 16 days, B takes 24 days. Total work = LCM(16,24) = 48 units. A/day = 3, B/day = 2. Working alternately starting with A for 10 days (5 cycles): work = 5×(3+2) = 25 units. Remaining 23 units: day 11 (A) does 3, day 12 (B) does 2, day 13 (A) does 3, day 14 (B) does 2, day 15 (A) does 3, day 16 (B) does 2, day 17 (A) does 3, day 18 (B) does 2, day 19 (A) does remaining 3. Total 19 days.

Multiple choice

Mohan can complete a work in 25 days. He worked for 5 days and left the work; and then Bhim completed the remaining work in 30 days. Had Bhim started the work and left it after 15 days. how much more time would Mohan have taken to complete the remaining work ?

  1. 7.5 days

  2. 11.5 days

  3. 12 days

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

Mohan's rate is 1/25 per day. In 5 days he completes 5/25 = 1/5 of work. Remaining 4/5 is done by Bhim in 30 days, so Bhim's rate is (4/5)/30 = 2/75 per day. If Bhim works 15 days first, he completes 30/75 = 2/5. Remaining 3/5 at Mohan's rate (1/25) takes (3/5)/(1/25) = 15 days. Option D is correct.

Multiple choice

If A can do ¼ of a work in 6 days and B can do 1/6 of the same work in 8 days, how much will A get if both work together and are paid Rs 360 in all?

  1. 120

  2. 72

  3. 150

  4. 140

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

A completes 1/24 of the work daily while B handles 1/48 per day. Working together, their combined rate is 1/16 per day. A's contribution ratio is (1/24)/(1/16) = 2/3, earning Rs 240 from the Rs 360 total, which is not listed in options A-D.

Multiple choice

A and B together can do a work in 20 days. B and C together can do the same work in 25 days. C and A together can do the same work in 15 days. A alone can do the same work in a day?

  1. 600/17

  2. 600/23

  3. 1200/23

  4. 1200/17
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given rates: A+B = 1/20, B+C = 1/25, C+A = 1/15 work per day. Adding all three equations: 2(A+B+C) = 1/20 + 1/25 + 1/15 = (15 + 12 + 20)/300 = 47/300. Therefore A+B+C = 47/600. To find A alone: A = (A+B+C) - (B+C) = 47/600 - 1/25 = 47/600 - 24/600 = 23/600 work per day. Thus A alone takes 600/23 days to complete the work. This is a standard combined work problem requiring algebraic manipulation of rates.

Multiple choice

P and Q together complete a work in 8 days. Q and R together complete a work in 16 days and R and P together complete the same work in 8 days. In how many days P, Q and R together can complete the wok?

  1. 7.1

  2. 7.2

  3. 6.4

  4. 5.8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P+Q = 8, so (P+Q)'s work = 1/8 per day. Q+R = 16, so (Q+R)'s work = 1/16 per day. R+P = 8, so (R+P)'s work = 1/8 per day. Adding all three equations: 2(P+Q+R) = 1/8 + 1/16 + 1/8 = 5/16, so P+Q+R = 5/32. Time for all three = 32/5 = 6.4 days.

Multiple choice

X, Y and Z takes 18 days to complete a piece of work. If X works alone he finishes the work in 36 days and If Y works alone he finishes the work in 60 days, how will it take Z to complete the work alone?

  1. 78

  2. 90

  3. 96

  4. 114
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Combined work rate of X, Y, Z is 1/18. X's rate is 1/36, Y's rate is 1/60. Z's rate = 1/18 - 1/36 - 1/60 = 10/180 - 5/180 - 3/180 = 2/180 = 1/90. Therefore, Z alone takes 90 days to complete the work.

Multiple choice

A, B and C, working alone can do a piece of work in 15, 30, and 75 days respectively. They work together and get Rs.1615 for completing the work. What is the difference in shares of A and C ?
  1. $Rs.760$
  2. $Rs.620$
  3. $Rs.680$
  4. $Rs.540$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work rates: A completes in 15 days (rate 1/15), B in 30 days (rate 1/30), C in 75 days (rate 1/75). Taking LCM of 150 as work units: A does 10 units/day, B does 5 units/day, C does 2 units/day. Total 17 units/day means work finishes in 150/17 days. Payment is divided in ratio 10:5:2, so A gets Rs. 950, C gets Rs. 190. Difference is Rs. 760.

Multiple choice

A can do 20% part of a work in 8 days, B works 30% part of the same work in 12 days and C works 40% part of that work in 18 days. If B and C's 1-day wage difference is Rs 12, then what will be the wage of A on working 35 days?

  1. 1080 Rs.

  2. 3500 Rs.

  3. 3780 Rs.

  4. 7000 Rs.

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

A does 20% work in 8 days → A's 1 day work = 20%/8 = 2.5%. B does 30% in 12 days → B's 1 day work = 30%/12 = 2.5%. C does 40% in 18 days → C's 1 day work = 40%/18 ≈ 2.22%. B and C work ratio is 2.5:2.22. B-C wage difference = Rs 12 for 1 day. A's wage for 35 days = (A's work/B's work) × (B's wage - C's wage) × 35 = (2.5/2.5) × 12 × 35 = Rs 3780.

Multiple choice

To complete a work, A and B take 30 days, B and C take 24 days, and C and A takes 20 days. They all start together and work for 5 days after which B and C leave. How many more days will A take to finish the remaining work?

  1. 11

  2. 28

  3. 33

  4. 18

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

Given: A+B=30 days, B+C=24 days, C+A=20 days. Combined rate (A+B+C)/2 = (1/30+1/24+1/20)/2 = (4+5+6)/120 × 1/2 = 15/240 = 1/16, so all three complete work in 16 days together. In 5 days they complete 5/16 of work. Remaining 11/16 done by A alone at rate (1/16 - 1/24) = (3-2)/48 = 1/48. Time = (11/16)/(1/48) = 11×3 = 33 days. Option C is correct.

Multiple choice

40 men can do a piece of work in a given time. If only 30 men be engaged, 6 more days are needed to complete the work. In how many days can 60 men do the work?

  1. 9

  2. 10

  3. 12

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

Let d be the number of days for 40 men. Work = 40d man-days. With 30 men: 30(d + 6) = 40d, so 30d + 180 = 40d, giving d = 18 days. Total work = 40 × 18 = 720 man-days. With 60 men: days = 720/60 = 12 days. Alternatively, 60 men is 1.5 times 40 men, so time is 18/1.5 = 12 days.