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

24 workers working 8 hours/day complete a work in 18 days. 30 workers working 6 hours/day will complete two-third of the work in how many days. 24 श्रमिक 8 घण्टे/दिन कार्य करके किसी कार्य को 18 दिनों में पूरा करते हैं। 30 व्यक्ति 6 घण्टे/दिन कार्य करके दो तिहाई कार्य को कितने दिनों में समाप्त करेंगे-

  1. 15 days/दिन

  2. 18 days/दिन

  3. 14.4 days/दिन

  4. 12.8 days/दिन
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 24×8×18 = 3456 man-hours. Two-thirds of work = 3456×(2/3) = 2304 man-hours. 30 workers at 6 hours/day do 180 man-hours per day. Days needed = 2304/180 = 12.8 days. This uses the standard work formula: Work = Men×Hours×Days, and we solve for the unknown days when the work quantity and workforce parameters change.

Multiple choice

Ram does a work in 40 days and Shyam does same work in 60 days. If efficiency of Mohan is 20% less than the combined efficiency of Ram and Shyam together then working alone Mohan will complete the whole work in how many days? राम किसी कार्य को 40 दिन में करता है तथा श्याम उसी कार्य को 60 दिनों में करता है। यदि मोहन की क्षमता राम तथा श्याम की संयुक्त क्षमता से 20 प्रतिशत कम है तो मोहन अकेले पूरे कार्य को कितने दिनों में करेगा?

  1. 24 days/दिन

  2. 30 days/दिन

  3. 32 days/दिन

  4. 27.5 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ram's efficiency: 1/40 work per day. Shyam's efficiency: 1/60 work per day. Combined efficiency = 1/40 + 1/60 = 5/120 = 1/24. Mohan's efficiency is 20% less = 80% of combined = 0.8 × 1/24 = 1/30. So Mohan alone takes 30 days. Verification: Combined (Ram + Shyam) do 1/24 per day. Mohan does 0.8 × 1/24 = 1/30 per day, so 30 days to complete.

Multiple choice

A does a work in 72 days. B who is 20% more efficient will complete 40% work in how many days? A किसी कार्य को 72 दिनों में समाप्त करता है। B जोकि A से 20% अधिक कार्य कुशल है 40 प्रतिशत कार्य को कितने दिनों मे समाप्त करेगा?

  1. 20 days/दिन

  2. 24 days/दिन

  3. 30 days/दिन

  4. 36 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A completes work in 72 days, so A's rate = 1/72 per day. B is 20% more efficient, so B's rate = 1.2 × 1/72 = 1/60 per day. B completes 40% (0.4) of work: Time = 0.4 ÷ (1/60) = 24 days. Verify: In 24 days, B does 24/60 = 40% of work.

Multiple choice

2 women and 1 boy can complete a piece of work in 14 days while 4 boys and 2 women can do the same work in 8 days. if a woman gets Rs.240 per day, then a boy will get per day-/2 महिलाएं और 1 लड़का एक कार्य को 14 दिनों में पूरा कर सकते हैं। जबकि 4 लड़के और 2 महिलाएं उसी कार्य को 8 दिन में पूरा कर सकते हैं। यदि एक महिला 240 रूपये प्रति दिन प्राप्त करती है तो एक लड़का प्रतिदिन प्राप्त करेगा-

  1. Rs. 120

  2. Rs. 150

  3. Rs. 165

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

Let woman's efficiency = w, boy's = b. From 2w + b = 1/14 and 2w + 4b = 1/8, subtracting gives 3b = 3/56, so b = 1/56. Then 2w = 1/14 - 1/56 = 3/56, giving w = 3/112. The ratio w:b = 3:2. If woman earns Rs. 240/day, boy earns 240 × 2/3 = Rs. 160/day. Option D is correct.

Multiple choice

Rajesh and Suresh completes a work in 45 days and 75 days respectively. Efficiency of Mohan is 40% more than the efficiency of Rajesh. Working all together they will complete the whole work in how many days?

  1. 20 days

  2. 24 days

  3. 18 days

  4. 15 days

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

Rajesh's 1 day work = 1/45. Suresh's 1 day work = 1/75. Mohan is 40% more efficient than Rajesh, so Mohan's 1 day work = (1/45) × 1.4 = 14/450 = 7/225. Combined work = 1/45 + 1/75 + 7/225. LCM = 225. Combined = (5+3+7)/225 = 15/225 = 1/15. Therefore, working together they complete the work in 15 days.

Multiple choice

A, B and C take a contract to do a piece of work. A can do it alone in 10 days. B can do it in 20 days and C can do it in 40 days. They work alternately. On the 1st day, A will do it alone, on the 2nd day, B will do it and on the 3rd day, C will do it alone and so on till the work is completed. Find the time in which work will be completed.

  1. 12 days

  2. 13.5 days

  3. 14 days

  4. 16.5 days

  5. 15 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: A = 1/10, B = 1/20, C = 1/40 per day. In a 3-day cycle: A + B + C = 7/40. After 5 cycles (15 days): 35/40 done, remaining = 5/40 = 1/8. Day 16 (A): 1/10 = 4/40, remaining = 1/40. Day 17 (B): needs only 1/40 of 1/20 = 0.5 day. Total = 16.5 days. Option D is correct.

Multiple choice

5 women can do a piece of work in 6 days while 10 boys can do it in 5 days. In how many days 5 boys and 3 women do it- 5 महिलाएं एक कार्य को 6 दिन में कर सकती है जबकि 10 लड़के इसी कार्य को 5 दिन में कर सकते हैं। 5 लड़के और 3 महिलाएं इसी कार्य को करेंगे-

  1. 10

  2. 5

  3. 8

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

5 women's 1 day work = 1/6, so 1 woman's 1 day work = 1/30. 10 boys' 1 day work = 1/5, so 1 boy's 1 day work = 1/50. Combined: 5 boys + 3 women = 5/50 + 3/30 = 1/10 + 1/10 = 1/5 work per day. So they take 5 days.

Multiple choice

A is 40% more efficient than B. C does half of the work done by A and B together. If C alone does the work in 36 days, then A, B and C together can do the work in ?

  1. 10 days

  2. 12 days

  3. 8 days

  4. 6 days

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

If A is 40% more efficient than B, then A:B efficiency ratio = 140:100 = 7:5. C does half the combined work of A and B, so C's efficiency = (7+5)/2 = 6 units. If C alone takes 36 days (C's total work = 6×36 = 216), then combined (A+B+C) efficiency = 7+5+6 = 18. Time = 216/18 = 12 days.

Multiple choice

A, B and C can finish a job working alone in 72, 24 and 36 days respectively. In how many days they can finish the job if they worked together? A, B और C अकेले काम करते हुए एक काम को क्रमशः 72, 24 और 36 दिनों में पूरा कर सकते हैं। यदि वे एक साथ काम करते हैं तो वे कितने दिनों में काम पूरा कर सकते हैं?

  1. 12

  2. 9

  3. 15

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

Individual rates: A = 1/72, B = 1/24, C = 1/36 work per day. Combined rate = 1/72 + 3/72 + 2/72 = 6/72 = 1/12 per day. Time = 1 / (1/12) = 12 days. This is a standard work-rate problem where rates add when working together.

Multiple choice

If the work done by (p-1) men in (p+1) days and the work done by (p+2) men in (p–1) days are in the ratio 9 : 10, then the value of p is equal to. (p-1) पुरूषों द्वारा (p+1) दिनों में किये गये कार्य और (p+2) पुरूषों द्वारा (p-1) दिनों में किये गये कार्य में अनुपात 9 : 10 है, तो p का मान है-

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work is proportional to both men and days, so work = k × men × days. Setting up the ratio: [(p-1)(p+1)] / [(p+2)(p-1)] = 9/10. Simplifying: (p+1)/(p+2) = 9/10. Cross-multiplying: 10p + 10 = 9p + 18. Solving: p = 8. The key insight is that work varies directly with both manpower and time.

Multiple choice

If Ram and Shyam together can complete a piece of work in 15 days and Shyam alone in 20 days, in how many days can Ram alone complete the work? यदि राम और श्याम एकसाथ मिलकर एक कार्य को 15 दिनों में पूरा करते हैं और श्याम अकेला इसे 20 दिनों में करता है, इस कार्य को राम कितने दिनों में पूरा कर सकता है?

  1. 60 days / दिन

  2. 45 days / दिन

  3. 40 days / दिन

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

Combined rate = 1/15 work per day. Shyam's rate = 1/20 work per day. Ram's rate = 1/15 - 1/20 = 4/60 - 3/60 = 1/60. Ram alone takes 60 days. The key is converting work time to rates and using subtraction.

Multiple choice

P and Q together can do a piece of work in 12 days. Q and R together do it in 15 days. If P's efficiency is twice that of R, then the days required for Q alone to finish the work is- / P और Q एक कार्य को एकसाथ मिलकर 12 दिन में कर सकते हैं। Q और R इसे 15 दिन में करते हैं। यदि P की कार्यक्षमता R की दोगुनी है, तो Q को कार्य को अकेले पूरा करने के लिए आवश्यक दिनों की संख्या है-

  1. 15 days / दिन

  2. 20 days / दिन

  3. 30 days / दिन

  4. 60 days / दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P=2x, Q=y, R=x (P is twice as efficient as R). P+Q = 1/12 work/day, Q+R = 1/15 work/day. Substituting: 2x+y = 1/12 and y+x = 1/15. Subtracting: x = 1/12 - 1/15 = (5-4)/60 = 1/60. So y = 1/15 - 1/60 = 4/60 - 1/60 = 3/60 = 1/20. Q's rate = 1/20, so Q alone takes 20 days. Verification: P=1/30, R=1/60, Q=1/20. P+Q=1/30+1/20=5/60=1/12 ✓, Q+R=1/20+1/60=4/60=1/15 ✓.

Multiple choice

X and Y together can complete a work in 12 days. X alone can complete in 20 days. If Y does the work only half a day daily, then in how many days X and Y together will complete the work? X और Y एक साथ 12 दिनों में एक काम पूरा कर सकते हैं। अकेले X, 20 दिनों में इसे पूरा कर सकता है यदि Y केवल प्रतिदिन आधे दिन काम करता है, तो कितने दिनों में X और Y एक साथ काम पूरा करेंगे?

  1. 10 days/दिन

  2. 20 days/दिन

  3. 11 days/दिन

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

Combined rate: X + Y = 1/12 work/day. X's rate = 1/20 work/day. So Y's rate = 1/12 - 1/20 = 1/30 work/day. When Y works half-day: effective rate = 1/20 + (1/30 × 1/2) = 1/20 + 1/60 = 4/60 = 1/15. Time = 15 days. Option D is correct.

Multiple choice

P and Q can complete a job in 24 days working together. P alone can complete it in 32 days. Both of them worked together for 8 days and then P left. The number of days Q will take to complete the remaining work is?

  1. 64 days

  2. 62 days

  3. 72 days

  4. 56 days

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

P+Q complete 1/24 of work per day. P alone does 1/32 per day, so Q alone does 1/24 - 1/32 = 1/96 per day. In 8 days together, they complete 8/24 = 1/3 of the work. Remaining 2/3 work is done by Q alone at rate 1/96, taking (2/3) / (1/96) = 64 days.

Multiple choice

A can do a piece of work in x days while B alone can do it in y days. With the help of C they can finish it in z days. If they are paid for Rs.960 for the whole work how much money A gets. It is given that y is 125% of x and z is one - third of y. A एक काम को x दिनों में कर सकता है जबकि B अकेला इसे y दिनों में कर सकता है | C की सहायता से वे इसे z दिनों में समाप्त कर सकते हैं | यदि वे पूरे काम के लिए रु.960 प्राप्त करते हैं, तो A कितना धन प्राप्त करता है| यह दिया गया है कि y, x का 125% है और z, y का एक - तिहाई है |

  1. Rs./रु.480

  2. Rs./रु.240

  3. Rs./रु.320

  4. Rs./रु.400
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

y = 1.25x, z = y/3 = x/3.75। A, B, C की दरें: 1/x, 1/1.25x, 3/x। संयुक्त दर = 1/z = 3.75/x = 1/x + 1/1.25x + C, से C की दर = 2/x। A की हिस्सेदारी = (1/x) / (3.75/x) = 4/15। A को मिलने वाला धन = 960 × 4/15 = 256 रु... पुनः गणना: z = y/3 = 5x/12। A, B, C दरें: 1/x, 4/5x, 12/5x। संयुक्त = 12/5x = 5/12x + 4/5x + C, से C = 109/60x। A का हिस्सा = (5/12x) / (12/5x) = 25/144। 960 × 25/144 = 166.67... कुछ गलत है।