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

If A is thrice efficient as C who is ½ efficient of B and the difference between time taken by A and C is 8 days then find the time taken by A and B together to complete the work? यदि A, C से तीन गुना कुशल है, जो B का ½ कुशल है और A और C द्वारा लिए गए समय के बीच का अंतर 8 दिन है, तो कार्य को पूरा करने के लिए A और B द्वारा एक साथ लिया गया समय ज्ञात कीजिए?

  1. 2.4 days 2.4 दिन

  2. 1.6 days 1.6 दिन

  3. 1.9 days 1.9 दिन

  4. 9 days 9 दिन

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

Let C's efficiency = 1 unit. Then A's efficiency = 3 units (A is thrice as efficient as C). B's efficiency = 2 units (C is half as efficient as B, so B is twice C). Time taken is inversely proportional to efficiency. If C takes t days, A takes t/3 days. Difference: t - t/3 = 2t/3 = 8 days, so t = 12 days. Therefore A takes 12/3 = 4 days alone. B takes 12/2 = 6 days alone. Together their rate = 1/4 + 1/6 = 5/12 work per day. Time together = 1 / (5/12) = 12/5 = 2.4 days. Option B (1.6) and C (1.9) are calculation errors, D (9) ignores efficiency.

Multiple choice

If A, B and C can complete a work in 6 days while A and B can complete the same work in 10 days and B and C can complete the same work in 12 days then find the time taken C to complete 60% of the work if he worked with 75% of its efficiency ? यदि A, B और C एक काम को 6 दिनों में पूरा कर सकते हैं, जबकि A और B उसी काम को 10 दिनों में पूरा कर सकते हैं और B और C उसी काम को 12 दिनों में पूरा कर सकते हैं, तो C को काम का 60% पूरा करने में लगने वाला समय ज्ञात कीजिए। यदि वह अपनी दक्षता के 75% के साथ कार्य करता है ?

  1. 12 days 12 दिन

  2. 15 days 15 दिन

  3. 18 days 18 दिन

  4. 10 days 10 दिन

  5. 16 days 16 दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let individual rates be A, B, C. Given: A+B+C=1/6, A+B=1/10, B+C=1/12. Subtracting: C=(A+B+C)-(A+B)=1/6-1/10=1/15. So C alone takes 15 days for full work. At 75% efficiency, C's rate becomes 0.75×(1/15)=1/20. For 60% of work: Time=0.6÷(1/20)=12 days. The calculations verify option A.

Multiple choice

48 persons can complete a work in 120 days. They started work and after x days 8 persons left the work. If the whole work was completed in 137 days, what is the value of x ?

  1. 42

  2. 45

  3. 35

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

Total work = 48 × 120 = 5760 person-days. Work done in x days by 48 persons = 48x. Remaining work done by 40 persons (8 left) in (137 - x) days = 40(137 - x). Setting up: 48x + 40(137 - x) = 5760, which simplifies to 8x = 280, giving x = 35. Option A (42) incorrectly assumes no productivity change, while Option D (24) would require 48×24 + 40×113 < 5760.

Multiple choice

Pramod can complete 66.6% of work while Shreya can complete 12.5% of the remaining work. The remaining work is completed by Ankit in 7 days. Find the time taken by Ankit to complete the same work.

  1. 12 days

  2. 24 days

  3. 36 days

  4. 16 days

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

Pramod does 66.6% = 2/3 of work. Remaining = 1/3. Shreya does 12.5% = 1/8 of remaining = 1/8 × 1/3 = 1/24 of total work. Remaining for Ankit = 1/3 - 1/24 = 7/24. Ankit completes 7/24 in 7 days, so total work takes 24 days. Option B correct.

Multiple choice

Akshay can do one-third of a Movie project in 15 days, Aamir can do 75% of the same movie project in 18 days and Ajay can do the same project in 36 days. Aamir and Ajay work together for 8 days. In how many days will Akshay alone complete the remaining Project?

  1. 20 days

  2. 18 days

  3. 17 days

  4. 12 days

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

Akshay's rate: (1/3)/15 = 1/45 per day. Aamir's rate: 0.75/18 = 1/24 per day. Ajay's rate: 1/36 per day. Aamir + Ajay combined: 1/24 + 1/36 = 5/72 per day. In 8 days they complete: 8 × 5/72 = 5/9 of work. Remaining: 1 - 5/9 = 4/9. Akshay's time: (4/9) / (1/45) = 20 days.

Multiple choice

Harry can do a piece of work in 24 days. Peter can do the same work in 30 days and Vinod in 40 days. Harry and Vinod worked for 4 days and handed it to Peter. Peter worked for some days and handed it again to Harry and Vinod 6 days before completing the work. For how many days did Peter work?

  1. 8 days

  2. 12 days

  3. 10 days

  4. 6 days

  5. 9 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Take total work as LCM(24,30,40) = 120 units. Harry does 5 units/day, Peter does 4 units/day, Vinod does 3 units/day. Harry and Vinod together do 8 units/day. They worked for 4 days initially and 6 days finally, totaling 10 days. Work done by H+V = 10 × 8 = 80 units. Remaining work = 120 - 80 = 40 units, done by Peter at 4 units/day, taking 40/4 = 10 days.

Multiple choice

Shridhar and Shravan together can do a work in 25 days. With the help of Pawan they completed the work in 8 days and earn Rs. 225 What is the share of Shravan if Shridhar alone can do the work in 75 days.?

  1. 42

  2. 48

  3. 53

  4. 43

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

Shridhar's 1-day work = 1/75, so Shravan's 1-day work = 1/25 - 1/75 = 2/75. With Pawan, 1-day work = 1/8, so Pawan's 1-day work = 1/8 - 1/25 = 17/200. Total 1-day work of all three = 1/75 + 2/75 + 17/200 = 3/75 + 17/200 = 1/25 + 17/200 = 25/200 = 1/8. Shravan's share = (2/75)/(1/8) × 225 = 16/75 × 225 = 16 × 3 = 48.

Multiple choice

Peter and Banner undertake a project worth Rs. 54000. Peter alone can do the work in 10 days. They work together for 3 days. After 3 days, Banner works alone for 3 days and Peter completes the remaining work in 3 more days. What is the share of Banner in the earnings?

  1. 21690

  2. 21600

  3. 22000

  4. 34000

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

Let Banner's rate be B/day. Peter's rate = 54000/10 = 5400/day. Total work: 3 days together (5400+B), 3 days Banner alone (B), 3 days Peter alone (5400) = 54000. Solving: 3(5400+B) + 3B + 3(5400) = 54000 → 32400 + 6B = 54000 → B = 3600/day. Banner works 6 days total (3 with Peter + 3 alone), earning 6 × 3600 = Rs. 21600.

Multiple choice

Kapil and Chandan together completed a work in 6 days. They got Rs. 1350 as remuneration. What would be the ratio in which the 1200 Rs would be split if Sunil worked along with Kapil and Chandan? I. Ratio of no: of days taken by Kapil & Sunil is 5:9 II. Ratio of efficiency of Kapil & Chandan = 3:2 III. Sunil is the least efficient of all.

  1. I only

  2. II only

  3. I & II

  4. I, II & III

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

Given Kapil+Chandan complete work in 6 days earning Rs.1350, we need to find how Rs.1200 would be split if Sunil joins. Statement I gives Kapil:Sunil days ratio (5:9), Statement II gives Kapil:Chandan efficiency (3:2). With I+II, we can determine individual efficiencies and calculate the new ratio. Statement III (Sunil least efficient) doesn't add needed quantitative data. Thus only I and II together are sufficient.

Multiple choice

Two persons Maddy and Mohan can do a work alone in 29 days. Maddy takes the rest of one day after every 4 days and Mohan takes the rest of one day after every 5 days. If Maddy and Mohan starts working together, then the work will be completed on

  1. 15th day

  2. 16th day

  3. 17th day

  4. 18th day

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

Maddy and Mohan together do 2/29 of work per day. After 16 days, Maddy worked 13 days (3 rests) and Mohan worked 13 days (3 rests). Total 26 days of work = 26 × 2/29 = 52/29 ≈ 1.79 times the work. This suggests completion on day 17 when Maddy works again.

Multiple choice

A group of men decided to do a job in 5 days, but 20 men dropped out every day. Find the number of men who initially decided to do the job, if the job was completed in 7 days?

  1. 140

  2. 120

  3. 210

  4. 190

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

Let W be the initial number of men and D be the total work. Each day, 20 men drop out, so day n has W - 20(n-1) men. Work done each day: (W-20) + (W-40) + ... + (W-120) = 7W - 420 = 5W (since 5W men would complete it in 5 days). Solving: 7W - 420 = 5W gives W = 210. The arithmetic progression of workers declining by 20 each day is the key insight.

Multiple choice

P and Q can do a piece of work in 14 days. Q and R together can do it in 21 days. If P is twice as good a workman as R, then in how many days Q alone can do the work?

  1. 42 days

  2. 40 days

  3. 35 days

  4. 38 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total work be LCM(14,21)=42 units. P+Q do 3 units/day and Q+R do 2 units/day. Since P is twice as efficient as R, let R=1 unit/day, then P=2 units/day. From Q+R=2, we get Q=1 unit/day. Q alone takes 42/1=42 days.

Multiple choice

A can do a certain work in 60 days. B is 25% more efficient than A, while C is 20% more efficient than B. B alone completed 37.5% of work. A and C together completed the remaining work. The entire work got completed in:

  1. 35 days

  2. 33 days

  3. 34 days

  4. 40 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1/60 work/day. B is 25% more efficient, so B's rate = 1.25 × 1/60 = 1/48 work/day. C is 20% more efficient than B, so C's rate = 1.2 × 1/48 = 1/40 work/day. B does 37.5% = 3/8 of work at rate 1/48, taking (3/8)/(1/48) = 18 days. Remaining work = 5/8 at rate (1/60 + 1/40) = 1/24, taking (5/8)/(1/24) = 15 days. Total = 18 + 15 = 33 days.

Multiple choice

A contractor decided to complete a work in 80 days and employed 60 men at the beginning and 20 men additionally after 20 days and got the work completed as per schedule. If he had not employed the additional men, how many extra days would he have needed to complete the work (round off to the nearest integer)?

  1. 32 days

  2. 26 days

  3. 30 days

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

Work = 60 × 20 + 80 × 60 = 4800 man-days. Without additional men: 60 × 80 would complete 4800 man-days, but we need to find when 60 men complete 4800 - 1600 = 3200 man-days. Time = 3200/60 = 53.33 days. Total would be 20 + 53.33 ≈ 73.33 days. Extra days = 73.33 - 80 = 6.67, but we need 80 - 60 = 20 more days total. Actually: 60 men in 100 days complete 4800. So extra = 100 - 80 = 20 days.

Multiple choice

If 6 boys or 12 girls can complete a piece of work in 24 days, then how many days will 5 boys and 8 girls take to complete the work?

  1. 20 days

  2. 18 days

  3. 14 days

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

6 boys complete work in 24 days, so 1 boy takes 144 days. 12 girls complete work in 24 days, so 1 girl takes 288 days. Work rate of 1 boy = 1/144 per day, 1 girl = 1/288 per day. Combined rate of 5 boys + 8 girls = 5/144 + 8/288 = 10/288 + 8/288 = 18/288 = 1/16 per day. Therefore, they complete the work in 16 days. Option A (20 days) would require a slower combined rate. Option B (18 days) and C (14 days) don't match the calculated rate.