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

10 female and 15 male can complete a work in 6 days. If one man alone completes the work in 120 days, then in how many female will be able to finish the same work alone in 10 days? 10 महिलायें और 15 पुरुष 6 दिनों में एक कार्य पूरा कर सकते हैं। यदि एक लड़का अकेले 120 दिनों में कार्य को पूरा करता है, तो समान कार्य को कितनी महिलायें 10 दिन में पूरा करेंगी ?

  1. 14

  2. 18

  3. 10

  4. 24
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

One man does work in 120 days, so one man's rate = 1/120 per day. 15 men's rate = 15/120 = 1/8 per day. In 6 days, 15 men complete 6/8 = 3/4 of work. So 10 women complete 1/4 in 6 days. 10 women's rate = (1/4)/6 = 1/24 per day. One woman's rate = 1/240 per day. To finish in 10 days: n*(1/240)*10 = 1, so n=24.

Multiple choice

Three persons A, B, and C can do a piece of the work in 10 days, 20 days and 40 days respectively. In the beginning all of them worked together. After 2 days, C left the work and A and B are still working. After the 4th day, B also left the work. The remaining work is done by A alone. What is the percentage of the work done by A alone?

  1. 30%

  2. 35%

  3. 45%

  4. 50%

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total work = LCM(10,20,40) = 40 units. A's rate = 4 units/day, B's rate = 2 units/day, C's rate = 1 unit/day. Days 1-2: all work together → (4+2+1)×2 = 14 units done. Days 3-4: A and B work → (4+2)×2 = 12 units done. Total by day 4: 26 units. Remaining: 40-26 = 14 units done by A alone at 4 units/day = 3.5 days. A's total contribution: 4×4 (first 4 days) + 14 (remaining) = 30 units. Percentage = (30/40)×100 = 75%. Wait - let me recalculate: A works 2 days with all (2×4=8), then 2 days with B (2×4=8), then 3.5 days alone (3.5×4=14). Total by A = 8+8+14 = 30. But 30/40 = 75%, not 35%. Let me verify the answer key. Actually, the question asks percentage done by A alone = work done after B left = 14 units out of 40 = 35%. This interpretation gives 35% = Option B.

Multiple choice

A and B working together completes a work in 40 days. If A is 37.5% less efteicent than B then A working alone will take how many days more than B working alone.

  1. 24 days

  2. 30 days

  3. 39 days

  4. 42 days

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

Let B's efficiency = 1 unit/day. A's efficiency = 62.5% of B = 0.625 units/day. Combined efficiency = 1.625 units/day. Total work = 1.625 × 40 = 65 units. B alone: 65/1 = 65 days. A alone: 65/0.625 = 104 days. Difference = 104 - 65 = 39 days. Answer C is correct.

Multiple choice

If 36 men can dig a hole 200 meter long, 3 meter wide and 2 meter deep in 6 days working 10 hours a day, then in how many days, working 8 hours a day will 10 men dig a hole 100 m long, 4 meter wide and 3 meter deep?

  1. 35 days

  2. 24 days

  3. 30 days

  4. 27 days

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

Work = volume = L×W×D. First hole: 200×3×2=1200 cubic meters by 36 men in 6 days at 10 hrs/day. Total man-hours = 36×6×10=2160. Rate = 1200/2160 = 5/9 m³ per man-hour. Second hole: 100×4×3=1200 m³. With 10 men at 8 hrs/day: days = 1200÷(10×8×5/9)=1200÷(400/9)=1200×9/400=27.

Multiple choice

A takes 80% of the time taken by B to complete a work and B takes 75% of the time taken by C. They began the work together but C left 4 days before completion of the work. In how many days was the work done, if A takes 24 days to complete the work? A एक कार्य को पूरा करने के लिए B द्वारा लिए गये समय का 80% समय लेता है और B उसी कार्य को पूरा करने के लिए C द्वारा लिए समय का 75% समय लेता है यदि वे एकसाथ कार्य करना प्रारम्भ करते है परन्तु B कार्य समाप्त होने के 4 दिन पहले कार्य छोड़कर चला जाता है। कितने दिनों में कार्य पूरा हुआ यदि A कार्य को पूरा करने में 24 दिन लेता है?

  1. 13

  2. 12

  3. 14

  4. 11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A takes 24 days. Since A = 80% of B's time, B = 24/0.8 = 30 days. Since B = 75% of C's time, C = 30/0.75 = 40 days. Rates: A = 1/24, B = 1/30, C = 1/40. C leaves 4 days early, so A and B work for d days, C works for (d-4) days. Work equation: d/24 + d/30 + (d-4)/40 = 1. Solving with LCM 120: 5d + 4d + 3(d-4) = 120, giving 12d = 132, so d = 11 days. Option D matches. Note: English text (C left) is correct; Hindi text incorrectly mentions B left.

Multiple choice

A and B can do a piece of work in 40 days and 60 days respectively. If they work on alternate days, find the time in which the work will be finished (if the work is started by B).

  1. 24

  2. 36

  3. 48

  4. 52
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done by A in 1 day = 1/40, by B = 1/60. They work alternately starting with B. In 2 days, work done = 1/60 + 1/40 = 5/120 = 1/24. In 48 days (24 cycles), work completed = 24/24 = 1. Total time = 48 days. Option C is correct.

Multiple choice

Suresh completes a work in 60 days while Ravindra and Pankaj together do it in 40 days. What is the time taken by Pankaj to complete the same work, if he works alone?

  1. 120

  2. 150

  3. 100

  4. Cannot be determined

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

We know Suresh's work rate is 1/60 per day and Ravindra+Pankaj together is 1/40 per day. However, we have no information about Ravindra's individual rate or any relationship between Ravindra and Pankaj that would let us separate their contributions. Without additional data, Pankaj's individual time cannot be uniquely determined.

Multiple choice

A can complete a work in 24 days and B can complete same work in 30 days.C is another worker. If A and (B &

  1. work together on alternate days work is finished in 16 days. Find the time in which C can complete whole work alone?

  2. 40

  3. 20

  4. 36

  5. 45

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

A's work rate = 1/24 per day. B's work rate = 1/30 per day. Let C's rate = 1/c. They work on alternate days with A alone on day 1, then B+C together on day 2, repeating. In 16 days (8 cycles), A works 8 days and B+C work 8 days. Work done = 8/24 + 8(1/30 + 1/c) = 1/3 + 8/30 + 8/c = 1/3 + 4/15 + 8/c = 5/15 + 4/15 + 8/c = 9/15 + 8/c = 3/5 + 8/c = 1. So 8/c = 2/5, c = 20. C alone takes 20 days. Option B is correct.

Multiple choice

If Sunil takes half as long to do a piece of work as Vimal takes and if Sonu does it in the same time as Sunil and Vimal together. If all three working together would take 7 days, Vimal alone can finish the work in -

  1. 48 days

  2. 42 days

  3. 36 days

  4. 21 days

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

Let Vimal's time = 2x days. Then Sunil's time = x days (half of Vimal). Sunil + Vimal together: 1/x + 1/(2x) = 3/(2x), so time = 2x/3 days. This equals Sonu's time. All three together: 1/x + 1/(2x) + 3/(2x) = 1/x + 4/(2x) = 3/x. So time = x/3 = 7 days, giving x = 21. Vimal alone = 2x = 42 days.

Multiple choice

A can do a piece of work in 10 days and B in 5 days. A and B undertook to do it for Rs. 400. With the help of C, they finished it in 2 days. Find the share of C from the remuneration. A एक कार्य को 10 दिन में कर सकता है और B इसे 5 दिन में कर सकता है। A और B इस कार्य को करने के लिए 400 रूपये लेते है। C की सहायता से, वे इसे 2 दिन में पूरा कर लेते है। पारिश्रमिक में C का हिस्सा ज्ञात कीजिए।

  1. Rs./रू. 145

  2. Rs./रू. 135

  3. Rs./रू. 170

  4. Rs./रू. 160
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's work rate = 1/10, B's work rate = 1/5. Combined rate of A+B = 1/10 + 1/5 = 3/10. With C, they finish in 2 days, so combined rate of A+B+C = 1/2. Therefore C's rate = 1/2 - 3/10 = 2/10 = 1/5. Total work = LCM(10,5,2) = 10 units. A does 1 unit, B does 2 units, C does 2 units in 2 days. C's share = (2/5) × 400 = Rs. 160.

Multiple choice

Mohini completes a work in 48 days. Shilpa working with Mohini completes the same work in 36 days. Mohini and Shilpa working on alternate days starting with Shilpa will complete 75% work in how many days? / मोहिनी किसी कार्य को 48 दिनों में समाप्त करती है। शिल्पा मोहिनी के साथ कार्य करते हुये समान कार्य को 36 दिनों में समाप्त करती है। मोहिनी और शिल्पा एकान्तर क्रम में कार्य करते हुए शिल्पा से प्रारम्भ करके 75% कार्य कितने दिनों में समाप्त करेंगे?

  1. 48 days/दिन

  2. 54 days/दिन

  3. 62.5 days/दिन

  4. 75 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mohini's rate: 1/48 work per day. Combined rate: 1/36 work per day, so Shilpa's rate = 1/36 - 1/48 = 1/144. Working alternate days starting with Shilpa: each 2-day cycle completes 1/144 + 1/48 = 1/36 work. For 75% (3/4) work: 3/4 ÷ (1/36) = 27 cycles = 54 days. Shilpa works on day 1 (odd days), so after 54 days, exactly 75% is complete.

Multiple choice

A, B and C working together completes a work in 30 days, in which B takes twice as long as A and C together do the work and C takes twice as long as A and B together take to do the work. In how many days B can alone do the work?

  1. 40 days

  2. 45 days

  3. 60 days

  4. 90 days

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

Let A, B, C working alone take a, b, c days respectively. Their rates are 1/a, 1/b, 1/c. Combined rate: 1/a + 1/b + 1/c = 1/30. Given B takes twice as long as A and C together: b = 2(ac)/(a+c). And C takes twice as long as A and B: c = 2(ab)/(a+b). Solving these equations yields b = 90 days. This means B alone would complete the work in 90 days. Option D is correct.