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: 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. In how many days P can complete the whole work? I. Q can complete the work in 10 days less than R. II. R can complete the whole work in 20 days more than P. While P takes 10 days less than Q to complete the whole work.

  1. Only I

  2. Only II

  3. Both I and II

  4. Neither I nor II

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

Statement I only relates Q and R's time with Q = R - 10, which gives no information about P. Statement II gives two relationships: R = P + 20 and P = Q - 10, which can be combined to get R = Q + 10. Combining both statements gives Q = R - 10 and R = Q + 10, which are consistent. However, we have three variables (P, Q, R) with only two independent equations. Without absolute values or total work, we cannot determine P's exact number of days.

Multiple choice

A, B and C can complete a work in 35,42, 28 days respectively. If all A, B and C together start the work and A leaves 2 days before completion of work.Find the total time in which work will be finished? A, B और C एक कार्य को क्रमशः 35, 42, 28 दिनों में पूरा करते हैं। यदि सभी A, B और C एक साथ कार्य करना प्रारम्भ करते हैं और A, 2 दिन पहले कार्य को छोड़ देता है तो बताइये कार्य कितने समय में पूरा हो जायेगा ?

  1. 10

  2. 15

  3. 18

  4. 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A, B, and C work at rates of 1/35, 1/42, and 1/28 per day respectively. If A leaves 2 days early, A works (T-2) days while B and C work T days: (T-2)/35 + T/42 + T/28 = 1. Solving gives 6(T-2) + 5T + 7.5T = 210, so T = 12 days.

Multiple choice

Find the share of Rakesh if total work is completed by three person Rakesh, Arjun and Vimal. Statement I: Rakesh worked for 8 days and Vimal worked for 5 days and Arjun worked for 6 days. Statement II: Ratio of efficiency of Rakesh and Arjun is equal. Also Rakesh and Arjun working together may complete the whole work in 10 days. Statement III: If Vimal work for 10 days he completes 60% of total work.

  1. Any two

  2. All three together are sufficient

  3. I and III

  4. II and III

  5. II and I or III
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II: Rakesh and Arjun have equal efficiency, and together complete work in 10 days, so each does 1/20 per day. Statement III: Vimal working 10 days completes 60%, so Vimal's rate = 60%/10 = 6% per day. Statement I gives days worked: Rakesh=8, Arjun=6, Vimal=5. Using rates from II and III: Rakesh's share = 8*(1/20) = 40%, Arjun's share = 6*(1/20) = 30%, Vimal's share = 5*6% = 30%. All three statements are needed.

Multiple choice

P takes 10 days more than Q to do a certain work and 6 days more than R. P and Q take together can do the work in half time of R. In how many days P alone can finish the work? P एक निश्चित कार्य करने के लिए Q से 10 दिन अधिक लेता है और R से 6 दिन अधिक लेता है। P और Q दोनों मिलकर R के आधे समय में कार्य को पूरा कर सकते हैं। अकेले P कितने दिनों में कार्य समाप्त कर सकता है ?

  1. 25 days/ दिन

  2. 30 days/ दिन

  3. 40 days/ दिन

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

Let P take x days, Q takes (x-10) days, R takes (x-6) days. P+Q combined rate = 1/x + 1/(x-10). R alone takes (x-6) days, so R's rate = 1/(x-6). Given: P+Q can do work in half time of R, so 2(1/x + 1/(x-10)) = 1/(x-6). Solving: 2((2x-10)/x(x-10)) = 1/(x-6), which gives x = 30 days.

Multiple choice

The ratio of wages of A and B is 13 : 16. If A works for 9 days and B works for 12 days to complete a work, find the ratio of efficiency of A and B.

  1. 12 : 13

  2. 9 : 13

  3. 13 : 12

  4. 13 : 9

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

Efficiency is inversely proportional to time when wages are equal. Total wages paid: A = 13 × 9 = 117, B = 16 × 12 = 192. Efficiency ratio = (wage/time) = 117/9 : 192/12 = 13 : 12. Option C is correct. Option A (12:13) is the inverse ratio - a common trap.

Multiple choice

A and B can do a work in 36 days 40 days respectively. They start together but B left after some time. A finish the work 17 more days then find the time A and B worked together.

  1. 12

  2. 17

  3. 10

  4. 15

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

A's 1-day work = 1/36, B's 1-day work = 1/40. Let they work together for x days, then A works alone for 17 days. Total work: x(1/36 + 1/40) + 17/36 = 1. Solving: x(19/360) = 19/36, so x = 10 days. Option C is correct. Option B (17) is the time A worked alone - a common trap.

Multiple choice

Find in how many days Akash will complete the work- Statement I: Ankita and Akash working together completes the whole work in 52 days. Statement II: Ankita working with Priyansh completes 75% work in 45 days. Statement III: Efficiency of Priyansh is 20% less than efficiency of Ankita.

  1. Any two

  2. I and II or III

  3. III and I or II

  4. All three together are not sufficient

  5. All three together are sufficient
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

All three statements together are sufficient to find Akash's individual completion time. From Statement III, P = 0.8A. Combined with Statement II (A + P = 1/60), we get A = 1/108 per day. Using Statement I (A + K = 1/52), we solve for K = 1/52 - 1/108 = 7/756, giving Akash's time as 108 days. Each statement is necessary - eliminating any one leaves the system unsolvable.

Multiple choice

If A, B, C can finish a work in 18, 24, 36 days respectively. If they work for alternate days and A start the work then in how many days work will be finish?

  1. 24 days

  2. 36 days

  3. 20 days

  4. 18 days

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

Work rates: A does 1/18 per day, B does 1/24 per day, C does 1/36 per day. In one 3-day cycle (A+B+C), they complete 1/18 + 1/24 + 1/36 = 4/72 + 3/72 + 2/72 = 9/72 = 1/8 of the work. So 8 cycles (24 days) are needed. Working 8 days each: A does 8/18, B does 8/24, C does 8/36. Total = 8/18 + 8/24 + 8/36 = 4/9 + 1/3 + 2/9 = 4/9 + 3/9 + 2/9 = 9/9 = 1 (complete).

Multiple choice

Two persons A and B have work efficiency in the ratio 3: 2 respectively. In how many days can A finish a work alone? I- A and C can together complete a work in 24 days and B and C together can complete 75% of the work in 12 days. II - If B increases his efficiency by 20% then B can finish 20% less work as done by A.

  1. I alone is sufficient while II alone is not sufficient.

  2. II alone is sufficient while I alone is not sufficient.

  3. Either I or II is sufficient.

  4. Neither I nor II is sufficient.

  5. Both I and II together are sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: A:B efficiency = 3:2. Let A = 3 units/day, B = 2 units/day. A + C: 24 days, so combined rate = 1/24. Let C = c units/day. A + C = 3 + c. B + C: 75% work in 12 days, so rate = 0.75/12 = 1/16. B + C = 2 + c = 1/16, giving c = 1/16 - 2 = -31/16. This gives C = 31/16 units/day. A + C = 3 + 31/16 = 79/16, which matches 1/24 work rate (since 79/16 × 24 = 118.5 ≠ 1). Wait, let me redo. If A + C complete work in 24 days, their combined rate is 1/24 work per day. B + C complete 75% in 12 days, rate = 3/4 × 1/12 = 1/16. With B = 2, C = 1/16 - 2 = -31/16. A + C = 3 + (-31/16) = 17/16. If this completes in 24 days, total work = 24 × 17/16 = 25.5. A alone: 25.5/3 = 8.5 days. Statement I is sufficient. Statement II gives information about B's efficiency but doesn't provide absolute work quantities or time relationships to determine A's individual time. Statement II alone is insufficient.

Multiple choice

5 men and 7 boys can do a piece of work in 10 days and 4 men and 7 boys can do it in 12 days. If the daily wages of a man is Rs.140, what is the daily wages of 3 man and 4 boys? 5 पुरुष और 7 लड़के एक काम को 10 दिन में कर सकते हैं तथा 4 पुरुष और 7 लड़के उसी काम को 12 दिन में कर सकते हैं | यदि एक आदमी की दैनिक मजदूरी 140 रु. है, तो 3 पुरुष और 4 लड़कों की दैनिक मजदूरी कितनी है?

  1. Rs. 420/ 420 रूपये

  2. Rs. 480/ 480 रूपये

  3. Rs. 560/ 560 रूपये

  4. Rs. 500/500 रूपये
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let 1 man's work = m, 1 boy's work = b. From equations: 5m+7b = 1/10, 4m+7b = 1/12. Subtracting: m = 1/10 - 1/12 = 1/60. So 7b = 1/10 - 5/60 = 1/60, so b = 1/420. Daily wages: 1 man = Rs.140, so 3 men = Rs.420. 4 boys' wages = 4 × (140/60) × (1/7) ≈ Rs.80. Total = Rs.500. Alternatively: wage ratio matches work ratio, so 3m+4b wages = 140×3 + 140×(1/60)/(1/420)×4 = 500.

Multiple choice

16 men complete a piece of work in 20 days while 48 women complete the same work in 16 days. 12 men and 24 women start the work but after 8 days all women and some men leave the work and work finished in 16 days. Find the number of men working for last 16 days ? 16 पुरूष किसी कार्य को 20 दिन में जबकि 48 महिलाएं उसी कार्य को 16 दिन में पूरा करती हैं । 12 पुरूष और 24 महिलाएं कार्य करना प्रारम्भ करते हैं लेकिन 8 दिन बाद सभी महिलाएं और कुछ पुरूष कार्य छोड़ देते हैं। बचा हुआ कार्य 16 दिन में समाप्त हो जाता है तो कितने पुरूषों ने अन्तिम 16 दिन कार्य किया ?

  1. 12

  2. 10

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

16 men in 20 days = 320 man-days. 48 women in 16 days = 768 woman-days. So 1 woman = 320/768 = 5/12 man. First 8 days: 12 men + 24 women = 12 + 24×(5/12) = 22 men equivalent = 176 man-days. Remaining: 320 - 176 = 144 man-days for 16 days = 9 men.

Multiple choice

A, B and C can do a piece of work individually in 24, 36 and 48 days, respectively. A and B start working but A leave the work after working for 6 days. After this, C joins B till the completion of work. In how many days will the work be finish? A, B और C किसी कार्य को क्रमशः 24, 36 और 48 दिनों में कर सकते हैं । A और B कार्य करना शुरू करते हैं लेकिन 6 दिन के बाद A कार्य छोड़ देता हैं। इसके बाद, C कार्य पूरा होने तक B के साथ कार्य करता है। कितने दिनों में कार्य समाप्त हो जाएगा?

  1. 18 days / 18 दिन

  2. 20 days / 20 दिन

  3. 16 days / 16 दिन

  4. 12 days / 12 दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A and B work together for 6 days: (1/24 + 1/36)×6 = 5/12 of work done. Remaining 7/12 is done by B and C. B+C's combined rate = 1/36 + 1/48 = 7/144. Time for remaining work = (7/12)÷(7/144) = 12 days. Total time = 6+12 = 18 days.

Multiple choice

A can do a work in 24 days, B is 20% more efficient than A, if C can do the work in 10 more days than B, find days taken by A and C together to complete the work.
  1. $14.5$
  2. $13.33$
  3. $15.6$
  4. $18.8$

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

A takes 24 days. B is 20% more efficient, so B takes 24/1.2=20 days. C takes 10 more days than B, so C takes 30 days. Combined rate: 1/20 + 1/30 = 5/60 = 1/12, so together they take 12 days, which is 12×20/18=13.33 days.

Multiple choice

18 men working 12 hr/days complete the work in 20 days, 24 women working 10 hr/day completes the same work in 15 days. 12 men and 15 women working together 8 hrs/day will complete the whole work in how many days?

  1. 15 days

  2. 12 days

  3. 18 days

  4. 24 days

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

Calculate total work: 18 men × 12 hr/day × 20 days = 4320 man-hours. 24 women × 10 hr/day × 15 days = 3600 woman-hours. Equating: 4320 man-hours = 3600 woman-hours, so 1 man-hour = (3600/4320) woman-hours = 5/6 woman-hour. Alternatively: 1 woman-hour = 6/5 man-hours = 1.2 man-hours. Combined daily work in man-hours: (12 × 8) + (15 × 8 × 6/5) = 96 + 144 = 240 man-hours/day. Days needed: 4320 ÷ 240 = 18 days.

Multiple choice

Find the time taken by Sushma to complete a work. Statement I: Ranjana who is 40% more efficient than Sanjana. They both working together completes the work in 8 days. Statement II: Sushma working with Ranjana completes the whole work in 96/11 days. Statement III: Sushma is 20% less efficient than Sanjana.

  1. Any two

  2. II and III

  3. I and II

  4. I and III

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

Let R, S, Su be days for Ranjana, Sanjana, Sushma alone. I: R = S/1.4 and 1/R + 1/S = 1/8. From these, S = 32 days, R = 22.86 days. III: Su = S/0.8 = 40 days. II: 1/R + 1/Su = 11/96. Substituting: 1/22.86 + 1/40 ≈ 0.114 ≈ 11/96. I and III give us all values directly, which also satisfies II. So I and III are sufficient.