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

P is twice as good as Q and together they finish a piece of work in 36 days. The number of days taken by P alone to finish the work? P, Q से दोगुना अच्छा है और एकसाथ वे 36 दिनों में एक काम पूरा करते हैं। कार्य समाप्त करने के लिए P द्वारा अकेले लिए गए दिनों की संख्या है?

  1. 48

  2. 60

  3. 54

  4. 72
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P is twice as good as Q means P's efficiency = 2 × Q's efficiency. Together they finish in 36 days. Combined efficiency = P + Q = 2Q + Q = 3Q. If 3Q takes 36 days, Q alone would take 36 × 3 = 108 days. P alone (who is twice as good) would take 108/2 = 54 days.

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?

  1. Rs. 420

  2. Rs. 480

  3. Rs. 560

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

Let work done by 1 man in 1 day = m and 1 boy = b. From the given: 10(5m + 7b) = 12(4m + 7b) = W. Solving gives m = 0.1W and b = W/84. Total work W = 84 units. Daily wage for 1 man = Rs.140 corresponds to 0.1W work, so per unit wage = Rs.140/8.4. Daily wages of 3 men and 4 boys = 3m + 4b = 0.3W + 4W/84 = (0.3 + 4/84)W = Rs.500. Option D is correct.

Multiple choice

X and Y undertook to do a piece of work for Rs.5400. X alone could do this work in 18 days and Y alone could do this work in 24 days. With the assistance of Z they finished the work in 8 days. What is the share (in Rs) of Z ? X और Y ने 5400 रुपये के लिए एक कार्य को किया। X अकेले 18 दिनों में इस काम को कर सकता है और Y अकेले 24 दिनों में इस कार्य को कर सकता है। Z की सहायता से वे 8 दिनों में काम समाप्त कर देते हैं। Z की हिस्सेदारी (रुपये में) क्या है?

  1. 1200

  2. 1500

  3. 1600

  4. 1800
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

X's rate = 1/18, Y's rate = 1/24. Combined rate of X+Y+Z = 1/8. Z's rate = 1/8 - 1/18 - 1/24 = (9-4-3)/72 = 2/72 = 1/36. Z's share = (1/36)×8×5400 = 1200.

Multiple choice

A can do a work in 15 days and B in 30 days. If they work on it together, then in how many days will they be able to do 50% of the work? A एक कार्य को 15 दिनों में और B उसे 30 दिनों में कर सकता है। यदि वे इस पर एक साथ काम करते हैं, तो वे कितने दिनों में 50% काम कर पाएंगे?

  1. 5

  2. 6

  3. 4

  4. 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's work rate is 1/15 per day, B's rate is 1/30 per day. Together they do 1/15 + 1/30 = 3/30 = 1/10 of the work per day. So they complete the full work in 10 days. For 50% of the work, they need 10 × 0.5 = 5 days.

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? P और Q एक साथ 8 दिनों में एक काम पूरा करते हैं। Q और R मिलकर एक काम को 16 दिन में पूरा करते हैं और R और P मिलकर उसी काम को 8 दिनों में पूरा करते हैं। P, Q और R एक साथ काम को कितने दिनों में पूरा कर सकते हैं?

  1. 6.4

  2. 7.2

  3. 5.8

  4. 7.1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P+Q = 1/8, Q+R = 1/16, R+P = 1/8 work per day. Adding all: 2(P+Q+R) = 1/8 + 1/16 + 1/8 = 5/16, so P+Q+R = 5/32 work per day. Time = 32/5 = 6.4 days. When all three work together, they complete the work faster. Options B, C, and D are incorrect estimates.

Multiple choice

Pinky and Puja together can do a piece of work in 24 days, which puja and Riya can do in 32 days. After Pinky has been working at it for 10 days and Puja for 14 days, Riya finishes it in 26 days. In how many days Riya alone will do the work?

  1. 12

  2. 24

  3. 36

  4. 48

  5. 60
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P, Pu, R be one-day work of Pinky, Puja, Riya. Given: P + Pu = 1/24, Pu + R = 1/32. After Pinky works 10 days, Puja works 14 days, and Riya finishes in 26 days: 10P + 14Pu + 26R = 1. Substituting P = 1/24 - Pu and solving: 4Pu + 26R = 7/12. Using Pu = 1/32 - R gives 26R - 4R = 7/12 - 1/8, so 22R = 11/24, thus R = 1/48. Therefore Riya alone takes 48 days.

Multiple choice

Efficiency of a man is twice of a boy while efficiency of a woman is two third of the man. If 8 boys can do a work in 20 days then find out the number of day in which 4 men and 6 women can finish this work?

  1. 20

  2. 15

  3. 30

  4. 10

  5. 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Boy's efficiency = 1 unit. Man = 2 × boy = 2 units. Woman = (2/3) × man = 4/3 units. Total work = 8 × 20 = 160 boy-days = 160 units. Combined efficiency of 4 men + 6 women = 4(2) + 6(4/3) = 8 + 8 = 16 units/day. Days = 160/16 = 10 days.

Multiple choice

Anju can do 3/4 of a job in 18 days. Prachi is twice as efficient as Anju. In how many days Prachi will complete the job? अंजू 18 दिनों में 3/4 कार्य कर सकती है। प्राची अंजू से दोगुनी कुशल है। प्राची कितने दिनों में काम पूरा करेगी?

  1. 12

  2. 10

  3. 8

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

Anju completes 3/4 of job in 18 days, so full job takes 18 × 4/3 = 24 days. Prachi is twice as efficient, so Prachi takes 24/2 = 12 days. Efficiency is inversely proportional to time taken.

Multiple choice

24 workers can do a piece of work in 18 days working 7 hours in a day. In how many hours working in a day 36 workers will do double of the same work in 14 days. 24 व्यक्ति 7 घंटे प्रतिदिन काम करके 18 दिन में एक कार्य पूरा करते हैं | 36 व्यक्ति कितने घंटे प्रतिदिन काम करके उसी काम का दोगुना कार्य 14 दिन में पूरा कर लेंगे?

  1. 10 hours/ घंटे

  2. 14 hours/ घंटे

  3. 8 hours/ घंटे

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

Work = workers × days × hours/day. Original work = 24 × 18 × 7 = 3024 work-hours. New work needed = 2 × 3024 = 6048 work-hours. Required hours/day = 6048 ÷ (36 × 14) = 6048 ÷ 504 = 12 hours. This uses the work formula and the inverse relationship between workers/hours and the direct relationship with amount of work.

Multiple choice

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work in 44 days. In how many days shall B finish the work alone? A और B मिलकर किसी कार्य को 30 दिन में पूरा कर सकते हैं। A, 16 दिन कार्य करता हैं और शेष कार्य B, 44 दिन में पूरा करता हैं। B कार्य को अकेले कितने दिनों में पूरा करेगा?

  1. 30

  2. 40

  3. 50

  4. 60
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A and B together do 1/30 of work per day. In 16 days, A does 16/A of work. Remaining work = 1 - 16/A. B completes this in 44 days at rate 1/B per day, so (1 - 16/A) = 44/B. Also 1/A + 1/B = 1/30. From the work equation: B(1 - 16/A) = 44, so B - 16B/A = 44. Since 1/A = 1/30 - 1/B, we get B - 16B(1/30 - 1/B) = 44, which gives B - 16B/30 + 16 = 44, so B(1 - 16/30) = 28, B(14/30) = 28, B = 28 × 30/14 = 60 days.

Multiple choice

Efficiency of A : B : C is 5 : 4 : 3, working together they can finish a work in 25 days. Then in how many days B and C together will take to do 35% of same work? A : B : C की दक्षता 5 : 4 : 3 है, एक साथ मिलकर वे 25 दिनों में एक काम खत्म कर सकते हैं तो कितने दिनों में B और C एक साथ मिलकर उसी काम का 35% समाप्त करेंगे?

  1. 15

  2. 12

  3. 10

  4. 18
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Efficiency ratio A:B:C = 5:4:3. Total efficiency working together = 5+4+3 = 12 units/day. Work completed in 25 days, so total work = 12 × 25 = 300 units. B and C's combined efficiency = 4+3 = 7 units/day. 35% of work = 0.35 × 300 = 105 units. Time for B and C to complete 105 units = 105/7 = 15 days.

Multiple choice

A and B together can do a piece of work in 12 days. If their shares of profit are Rs. 1443 and Rs. 962 respectively, then find in how many days A alone can complete the work?

  1. 20

  2. 30

  3. 25

  4. 18
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A and B together complete work in 12 days. Their profit shares (1443:962 = 3:2) reflect their work rates. If A's work rate is 3x and B's is 2x, then (3x + 2x) × 12 = 1 job, so 60x = 1. A alone takes 1/(3x) = 1/(3/60) = 20 days. Profit sharing is directly proportional to work contribution in partnerships.

Multiple choice

Amit can do 3 4th of work in 5 6 days in comparison to Bhanu. If both complete the work in 10 days doing together then in how many days Bhanu alone can finish the work?

  1. 18

  2. 21

  3. 19

  4. 21.5

  5. 22
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If Amit does 3/4 of work in 5/6 of Bhanu's time, Amit's rate : Bhanu's rate = (3/4)/(5/6) = 9:10. Together in 10 days: (9+10)/10k = 1/10, so k = 1. Bhanu alone: 10/1 = 10 days for full work. But wait - let me recalculate. Amit's efficiency = (3/4 work)/(5/6 time) = 9/10 of Bhanu. So if Bhanu takes x days, Amit takes x/(9/10) = 10x/9 days. Together: 1/x + 9/(10x) = 1/10. 19/(10x) = 1/10, x = 19. Bhanu takes 19 days.

Multiple choice

Quantity I: No. of days in which A will work alone, given A and B can complete work in 8 days, B and C can complete work in 12 days, C and A can complete work in 8 days. Quantity II: No. of days in which A will work alone, given A and B can complete work in 18 days, they started work together and after working for 6 days A left and B completed remaining work in 24 days.

  1. Quantity II < Quantity I

  2. Quantity II > Quantity I

  3. Quantity II ≤ Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity II = Quantity I or relation cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: 1/A + 1/B = 1/8, 1/B + 1/C = 1/12, 1/C + 1/A = 1/8. Adding first and third: 2/A + 1/B = 1/4. Subtract second: 2/A - 1/C = 1/6. But 1/A = 1/8 - 1/B, so A alone = 9.6 days. Quantity II: A+B work = 6/18 = 1/3. Remaining = 2/3 done by B in 24 days, so 1/B = (2/3)/24 = 1/36, B = 36 days. Then 1/A = 1/18 - 1/36, A = 36 days. Quantity II (36) > Quantity I (9.6).

Multiple choice

A work is started by a man and it is assumed that he will finish the work in 11 days if working alone. Each subsequent day a new man joined the work. In how many days the four times the original work will be completed, if after the 8th day from the starting of the work no new man will be further added?

  1. 5

  2. 6

  3. 7

  4. 8

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

One man completes 1/11 of the work per day. On day n, n men work, completing n/11 of the work. After day 8, no new men are added, so 9 men work from day 9 onwards. Sum of work from day 1 to day 8 is the sum of 1/11 to 8/11 = (1+2+...+8)/11 = 36/11. From day 9 onwards, 9 men work, so they complete 9/11 per day. To complete 4 times (44/11) of the work: 36/11 + 9/11 = 45/11, which exceeds 44/11, so the work completes on day 9.