CBSE Class 10 Mathematics Time and Work MCQs Set 19

Multiple Choice Questions (MCQs) for Class 10 Mathematics: Time and Work

Access targeted multiple-choice questions for Time and Work designed to align with the latest CBSE academic syllabus for Class 10 Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Practice Time and Work MCQs for Class 10 Mathematics

Navigate directly to the 50 objective questions for Time and Work using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: A pipe can fill a tank in 15 hours. The tank develops a hole and 10% of the water leaks out. The pipe will now fill the tank in
(a) 16 hrs 40 minutes
(b) 18 hrs 40 minutes
(c) 20 hrs
(d) 17 hrs 30 minutes
Show Answer & Explanation

Answer: (a) 16 hrs 40 minutes

Explanation:
1. Because 10% of the water leaks away, only 90% of the water stays
2. Time = 15/0.9 = 16 2/3 hrs = 16 hrs 40 minutes.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 2: Meena can type 500 words in 10 minutes and Leena can type 400 words in 10 minutes. They can together type 3600 words in
(a) 50 minutes
(b) 40 minutes
(c) 80 minutes
(d) 100 minutes
Show Answer & Explanation

Answer: (b) 40 minutes

Explanation:
1. Meena types 50 words/min and Leena types 40 words/min, so together 90 words/min
2. Time = 3600/90 = 40 minutes.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 3: A, B and C are employed to do a piece job for Rs. 529. A and B together are supposed to do 19/23 of the work. C should be paid
(a) Rs. 115
(b) Rs. 92
(c) Rs. 200
(d) Rs. 250
Show Answer & Explanation

Answer: (b) Rs. 92

Explanation:
1. C's part = 1 − 19/23 = 4/23
2. C's payment = 4/23 × 529 = Rs. 92.

Teacher's Note:
1. Payment is proportional to the work done.

Question 4: Sixteen men can complete a work in fifteen days. Twenty-four children can do the same work in twenty days. In how many days will eight men and eight children together complete the same job?
(a) 16
(b) 15
(c) 20
(d) None of the above
Show Answer & Explanation

Answer: (c) 20

Explanation:
1. One man does 1/240 per day and one child does 1/480 per day
2. 8 men + 8 children: 8/240 + 8/480 = 1/30 + 1/60 = 1/20
3. They take 20 days.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 5: Ram can complete a work in 12 days, while Rajan can finish it in 18 days. Ram works on it for 8 days and then Rajan starts working on it. Then the work will be finished in
(a) 6 days
(b) 7 days
(c) 8 days
(d) 9 days
Show Answer & Explanation

Answer: (a) 6 days

Explanation:
1. Ram does 8/12 = 2/3 of the work
2. Remaining 1/3 is done by Rajan in 18/3 = 6 days.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 6: B is twice as fast as A. If A can complete a job in 36 days, how long will it take for both A and B together to complete the same job?
(a) 24 days
(b) 18 days
(c) 12 days
(d) 9 days
Show Answer & Explanation

Answer: (c) 12 days

Explanation:
1. B takes 18 days
2. Together: 1/36 + 1/18 = 1/12 per day, so 12 days.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 7: A contractor undertakes to make a road in 72 days and employs 24 men. After 48 days, he finds that only half of the road is made. How many extra men should he now employ to complete the road in time?
(a) 36 men
(b) 24 men
(c) 21 men
(d) None of these
Show Answer & Explanation

Answer: (b) 24 men

Explanation:
1. 24 men made half the road in 48 days, so the remaining half in 24 days needs 24 × 48/24 = 48 men
2. Extra men = 48 − 24 = 24.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 8: 20 men working 9 hours per day can complete a work in 12 days. To complete the same work in 15 days working 12 hours a day, the number of men required is
(a) 15
(b) 14
(c) 12
(d) 11
Show Answer & Explanation

Answer: (c) 12

Explanation:
1. Total work = 20 × 9 × 12 = 2160 man-hours
2. N × 12 × 15 = 2160, so N = 12 men.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 9: A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in
(a) 4 days
(b) 6 days
(c) 8 days
(d) 12 days
Show Answer & Explanation

Answer: (c) 8 days

Explanation:
1. C = 1/6 − 1/8 = 1/24 and A = 1/6 − 1/12 = 1/12
2. A + C = 1/12 + 1/24 = 1/8, so 8 days.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 10: A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is
(a) 1/4
(b) 1/10
(c) 7/15
(d) 8/15
Show Answer & Explanation

Answer: (d) 8/15

Explanation:
1. Work in one day = 1/15 + 1/20 = 7/60
2. In 4 days = 28/60 = 7/15
3. Left = 8/15.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 11: Two pipes A and B can fill a tank in 24 min and 32 min respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 18 minutes?
(a) 7 min
(b) 8 min
(c) 9 min
(d) 10 min
Show Answer & Explanation

Answer: (b) 8 min

Explanation:
1. A works 18 minutes: 18/24 = 3/4
2. B must fill the remaining 1/4: t/32 = 1/4, so t = 8 min.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 12: A can do a piece of work in 10 days and B can do it in 15 days. After they have worked together for 4 days, A goes away and B completes the remaining work. In how many days does B complete the remaining work?
(a) 10
(b) 5
(c) 15
(d) 20
Show Answer & Explanation

Answer: (b) 5

Explanation:
1. Together in 4 days: 4 × (1/10 + 1/15) = 4 × 1/6 = 2/3
2. Remaining 1/3 takes B 15/3 = 5 days.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 13: A is twice as efficient as B and they together can complete a piece of work in 24 days. Find the number of days that A alone takes to complete the work.
(a) 36
(b) 18
(c) 48
(d) 30
Show Answer & Explanation

Answer: (a) 36

Explanation:
1. A + B = 1/24 with A = 2B gives 3B = 1/24, so B = 1/72 and A = 1/36
2. A alone takes 36 days.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 14: Working individually, A, B and C can finish a piece of work in 16, 20 and 30 days respectively. In how many days can A, B and C together complete a work which is 3 1/2 times the previous work?
(a) 30
(b) 25
(c) 24
(d) 20
Show Answer & Explanation

Answer: (c) 24

Explanation:
1. Together in one day: 1/16 + 1/20 + 1/30 = 35/240 = 7/48
2. One work takes 48/7 days, so 3.5 works take 3.5 × 48/7 = 24 days.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 15: Nitu alone can complete 4/5th of a piece of work in 20 days. She works for 6 days and Deepak replaces her. He completes the work in another 38 days. In how many days can Deepak complete the entire work if he works alone?
(a) 50
(b) 25
(c) 30
(d) 45
Show Answer & Explanation

Answer: (a) 50

Explanation:
1. Nitu does the whole work in 25 days, so in 6 days she does 6/25
2. Remaining 19/25 takes Deepak 38 days, so the whole takes 38 × 25/19 = 50 days.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 16: A certain number of people can complete a piece of work in 12 days working 5 hours a day. If the number of men is decreased by half, how many hours a day should they work, so that the work is to be completed in 15 days?
(a) 10
(b) 9
(c) 8
(d) 6
Show Answer & Explanation

Answer: (c) 8

Explanation:
1. N × 12 × 5 = (N/2) × 15 × h
2. 60 = 7.5h, so h = 8 hours a day.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 17: A can work twice as fast as B. A and C together can work three times as fast as B. If A, B and C complete a job in 30 days working together, in how many days can each of them complete the work (A, B, C respectively)?
(a) 40, 80, 100
(b) 60, 120, 120
(c) 50, 100, 120
(d) 60, 100, 80
Show Answer & Explanation

Answer: (b) 60, 120, 120

Explanation:
1. A = 2B and A + C = 3B give C = B
2. A + B + C = 4B = 1/30, so B = C = 1/120 and A = 1/60
3. A takes 60 days, B and C take 120 days each.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 18: P, Q and R started a piece of work. They worked on it for 5 days, after which P left. The other two continued to work for another 5 days after which Q left and the remaining work was completed by R in another 5 days. If Q alone can complete the work in 30 days and R alone takes more than 45 days to complete the work, who completed the maximum part of the work?
(a) P
(b) Q
(c) R
(d) Cannot be determined
Show Answer & Explanation

Answer: (a) P

Explanation:
1. Total work: 5p + 10q + 15r = 1 with q = 1/30, so 5p + 15r = 2/3
2. Q's part = 10/30 = 1/3
3. R's part = 15r < 15/45 = 1/3 and P's part = 5p = 2/3 − 15r > 1/3
4. P completed the maximum part.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

Question 19: A garrison had provisions for 1500 men for 30 days. After some days, 300 more men joined the garrison. The provisions lasted for a total of 26 days from the beginning. After how many days did the new men join?
(a) 24
(b) 6
(c) 4
(d) 26
Show Answer & Explanation

Answer: (b) 6

Explanation:
1. After d days the food left = 1500(30 − d) man-days
2. It feeds 1800 men for 26 − d days: 1500(30 − d) = 1800(26 − d)
3. 45000 − 1500d = 46800 − 1800d, so d = 6 days.

Teacher's Note:
1. Treat the whole work as 1; a person finishing in n days does 1/n of the work per day.
2. Add the daily work of people working together and take the reciprocal for the time.

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Time and Work Objective Questions & Solutions for Class 10 Mathematics

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FAQs

Where can I access latest CBSE Class 10 Mathematics Time and Work MCQs Set 19?

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Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics Class 10 material?

Yes, our CBSE Class 10 Mathematics Time and Work MCQs Set 19 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the CBSE paper is now competency-based.

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