Quick Test On Time & Work

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| By Divyanaidu94
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Divyanaidu94
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Quizzes Created: 10 | Total Attempts: 31,114
| Attempts: 374 | Questions: 25 | Updated: Mar 19, 2025
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1. M can do a piece of work in 24 days. He works at it alone for 4 days and N alone finishes the remaining work in 25 days. Both of them together can complete the work in?

Explanation

M can do the work in 24 days
∴ M can do in 4 days = 4/24 = 1/6 part
∴ Remaining work = 1 – 1/6 = 5/6
Since 5/6 is completed by N in 25 days
∴ 1 work is completed by N in 6/5 X 25 = 30 days
∴ Both together can do in 1 day = 1/24 + 1/30
= 5 + 4/120
= 9/120
∴ Hence both M and N can do the work in 120/9 = 13 3/9 = 13 1/3 days.

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About This Quiz
GMAT Quantitative Reasoning Quizzes & Trivia

Time and Work is one of the important topics in Quantitative Aptitude. In all competitive exams, we can expect a minimum of two questions from this topic. Practice this test and also share with your friends.

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2. 36 men can complete a work in 24 days. How many persons will be required to complete the work in 18 days?

Explanation

Required no. of persons = 36 X 24/18 = 48 persons.

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3. A, B and C each working alone, can finish a project in 42 days, 28 days and 48 days respectively. A started the project by working alone for 7 days and then B took over from A. B worked alone for 7 days, and then C took over from B. In how many days will C finish the remaining work?

Explanation

Let the total work be 336 units (LCM of 42, 28 and 48 = 336 units)
∴ A's one day's work = 336/42 = 8 units
Similarly, B's one day's work = 336/28 = 12 units
C's one day's work = 336/48 = 7 units
∴ A's 7 day's work = 7 X 8 = 56 units
B's 7 day's work = 7 X 12 = 84 units
∴ Remaining work = 336 - (56 + 84) = 196
∴ C can do the remaining work in 196/7 = 28 days.

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4. 12 persons can complete a piece of work in 84 days. How many persons will be required to complete the work in 36 days?

Explanation

Required no. of persons = 12 X 84/36 = 28 persons.

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5. If 20 men or 40 women or 80 children can do a piece of work in 11 days, then 5 men, 10 women and 15 children together can do the double of the work in __________

Explanation

20 men = 40 women = 80 children
∴ 1 man = 2 women = 4 children
∴ 1 woman = 2 children
∴ 5 men + 10 women + 15 children = 20 + 20 + 15 = 55 children
Now, M1D1 = M2D2
80 X 11 = 55 X D2
∴ D2 = 80 X 11/55
∴ D2 = 16 days.

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6. If 21 men can do a piece of work in 25 days working 10 hours a day, then how many men are required to complete the work in 15 days by working 7 hours per day?

Explanation

M1 X D1 X H1 = M2 X D2 X H2
M2 = M1 X D1 X H1/H2 X D2 = 21 X 25 X 10/15 X 7 = 50 men.

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7. Priyanka can do 3/4 of a job in 12 days. Muskan is twice as efficient as Priyanka. In how many days can Muskan finish the job?

Explanation

Priyanka can do the whole job in 12 X 4/3 = 16 days
∴ Muskan can do it in 16/2 = 8 days.

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8. When 24 men work for only 3 days, 5/6 of the work remains unfinished. How much work will remain unfinished if 27 men work for only 2 days?

Explanation

M1D1/W1 = M2D2/W2
Here M1 = 24, D1= 3 days, W1 = 1 – 5/6 = 1/6 work finished
M2 = 27, D2 = 2 days, W2 = ?
∴ W2 = M2D2 X W1/M1D1 = 27 X 2 X 1/6 / 24 X 3 = 9/24 X 3 = 1/8 work finished
∴ Unfinished work = 1 – 1/8 = 7/8.

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9. 8 children and 10 men complete a certain piece of work in 29 days. If each child takes twice the time taken by a man to finish the work, then in how many days will 15men and 86 boys finish the same work?

Explanation

2 children = 1 man
∴ 8 children and 10 men = 4 + 10 = 14 men
15 men + 86 boys = 15 men + 43 men = 58 men
58 men finish the work in 14X29/58 = 7 days.

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10. A and B can do a piece of work in 20 days while B and C can do the same piece of work in 30 days and C and A in 24 days. They all worked together for 10 days when C and A left the job. How many more days will B take to finish the work?

Explanation

2 (A + B + C)’s 1 day’s work = 1/20 + 1/30 + 1/24 = 15/120 = 1/8
∴ (A + B + C)’s 1 day’s work = 1/16
Work done by A, B and C in 10 days = 10/16 = 5/8
Remaining work = 1 – 5/8 = 3/8 part of work
∴ B’s 1 day’s work = 1/16 – 1/24 = 1/48
So, 3/8 part of the work will be done by B in 48 X 3/8 = 18 days.

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11. 18 men and 24 women can complete a piece of work in 16 days. All of them started working together but after 12 working days, the women stopped working together. 12 men completed the work in 9 days. How many days will it take to complete the entire job if only 24 women have to complete the job?

Explanation

Amount of work done by 18 men and 24 women in 12 days = 12/16 = 3/4
∴ Remaining work = 1 – 3/4 = 1/4
Now, 12 men complete ¼ work in 9 days
∴ 18 men can complete the entire work in 9 x 4 X 12/18 = 24 days
Now, 1/16 – 1/24 = 1/48
∴ 24 women together can do the job = 48 days.

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12. 8 men and 4 women together can complete a piece of work in 8 days. The work done by a man in one day is twice the work done by a woman in one day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined, in how many more days will the work be completed?

Explanation

According to the question,
1 man = 2 women
∴ 8 men = 2 X 8 = 16 women
∴ 8 men + 4 women = 16 + 4 = 20 women
4 men + 8 women = 8 + 8 = 16 women
20 women’s 2 days work = 2/8 = ¼ part
∴ Remaining work = 1 – ¼ = ¾
20 women complete 1 work in 8 days
∴ 16 women complete 1 work in 20 X 8/16 X 3/4
= 15/2 = 7 ½ days.

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13. 4 men can complete a piece of work in 7 days. 7 children can complete the work in 16 days. In how many days can 3 men and 2 children together complete the work?

Explanation

According to the question,
The work completed by one man and one child.
(4 X 7) men = (16 X 7) children
28 men = 112 children
∴ 1 man = 4 children
∴ 3 men = 3 X 4 = 12 children
Since, 7 children complete the work in 16 days.
∴ 12 + 2 = 14 children complete the work in 16 X 7/14 = 112/14 = 8 days.

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14. 24 women take 14 days to complete a piece of work which can be completed by 14 men in 12 days. 18 men started working and after 5 days, 10 men left and 8 women joined them. How many days will it take them to complete the remaining work?

Explanation

Work done by 24 women in 14 days = work done by 14 men in 12 days
(24 X 14) women = (14 X 12) men
∴ 2 women = 1 man
Now, work done by 14 men in one day = 1/12
1 man's 1 day's work = 1/12 X 14 = 1/168
∴ 18 men's 5 days work = 18 X 5/168 = 15/28
∴ Remaining work = 1 - 15/28 = 13/28
Now, 13/28 work is done by 8 men and 8 women
8 men + 8 women = (8 men + 4 men) = 12 men
Applying formula, M1D1/W1 = M2D2/W2
14 X 12/1 = 12 X D2/ 13/28
∴ D2 = 14 X 12 X 13/12 X 28 = 13/2 = 6 1/2 days.

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15. A certain number of men can complete a piece of work in 70 days. Had there been 12 men less, it would have taken 10 days more. How many men were there initially?

Explanation

Let initially the number of men be x
Then x men do the work in 70 days
Now, (x – 12) men do the work in (70 + 10) = 80 days
Thus, 70x = (x – 12) X 80
70x = 80x – 960
10x = 960
∴ x = 96 men.

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16. Two workers A and B working together completed a job in 12 days. Had A worked 4 times as efficiently as he actually did and B worked 2/3 as efficiently as he actually did, the work would have been completed in 7 days. To complete the job alone A would require?

Explanation

If A alone does the work in x days and B alone does the work in y days
Then, 1/x + 1/y = 1/12 ---------- > (i)
Again, 4/x + 2/3y = 1/7 ---------- > (ii)
Subtracting equation (i) from equation (ii) X 3/2 , we get
6/x + 1/y – 1/x – 1/y = 3/14 – 1/12
6/x – 1/x = 11/84
5/x = 11/84
∴ x = 84 X 5/11 = 38 2/11 days.

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17. 6 men and 6 women together can complete a piece of work in 6 days. In how many days can 15 men alone complete the same work if 9 women alone can complete it in 10 days?

Explanation

Since, 9 women can complete the work in 10 days
∴ 6 women can complete the work in 10 X 9/6 = 15 days
6 women in 6 days complete 6/15 = 2/5 part
∴ The remaining (1 – 2/5) = 3/5 part will be completed by 6 men in 6 days
So, 6 men’s work in 1 day = 3/5 X 6 = 1/10 part
Since, 6 men can complete the work in 10 days
∴ 15 men can complete the work in 6 X 10/15 = 4 days.

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18. Aman alone can complete a piece of work in 8 days. The work done by Bihubati alone in one day is half of the work done by Aman alone in one day. In how many days can the work be completed if Aman and Bihubati work together?

Explanation

X does the work in 8 days
Y does the work in 16 days
∴ X + Y do the work in 8 X 16/8 +16 = 5 1/3 days.

Submit
19. A can do a piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 days of which has been destroying. How many days must A now work alone to complete the work?

Explanation

A can do the work in 8 days
B can destroy it in 3 days
LCM of 8 and 3 is 24
So, A can do the work in 1 day = 3 units
B can destroy the work in 1 day = 8 units
Now, A has done the work in 6 days = 6 X 3 = 18 units
But B has been destroyed the work in 2 days
= 2 X 8 = 16 units
∴ In 8 days the work completed = 18 – 16 = 2 units
∴ Remaining work = 24 – 2 = 22 units
∴ 22 units of work is done by A in 22/3 = 7 1/3 days.

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20. Priyanka can do a piece of work in 4 hours. Priya and Pritam together can do it in 3 3/7 hours, while Priyanka and Pritam together can do it in 2 2/3 hours. How long will Priya alone take to do it?

Explanation

Priya + Pritam = 3 3/7 = 24/7 ------- > (i)
Priyanka + Pritam = 2 2/3 = 8/3 ------ > (ii)
Now, from (ii), we get
Pritam’s work = 3/8 – 1/4 = 3 – 2/8 = 1/8
Again from (i),
Priya’s work = 7/24 – 1/8 = 7 – 3/24 = 4/24 = 1/6
Hence Priya alone does it in 6 hours.

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21. A contractor undertook to do a certain work in 75 days and employed 48 men to do it. After 55 days he found that only 2/3 of the work was done. How many more men must be employed so that the work may finished in time?

Explanation

M1D2/W2 = M2 D2/W2
48 X 55/ 2/3 = M X 20/ 1/3
∴ M = 66 men
Required more men = 66 - 48 = 18 men.

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22. A alone can finish a piece of work in 36 days. B is 20% more efficient than A. C is 50% more efficient than B. In how many days can A and C working together finish the same piece of work? (in days)

Explanation

A can alone finish the work in 36 days
B is 20% more efficient than A
Then B can alone finish the work in 36 X 100/120
= 36 X 5/6 = 30 days
∴ C can alone finish the work in 30 X 100/150
= 30 X 4/6 = 20 days
∴ (A + C) can do it one day = 1/36 + 1/20
= 5 + 9/180
= 14/180 = 7/90
∴ A and C can finish the work in 90/7 = 12 6/7 days.

Submit
23. A can build up a structure in 8 days and B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days. In how many days will A alone build up the remaining part of the structure?

Explanation

A can build the structure in 8 days
∴ A can build the structure in a day = 1/8 part
Similarly, B can break the structure in 3 days
∴ B can break 1/3 part of structure in 1 day
Amount of work done by A in 4 days = 4/8 = 1/2
Again, both A and B together work for 2 days
So, the part of work done in these 2 days
= 2 (1/8 – 1/3) = - 5/12
∴ Remaining work = 1 – 1/2 + 5/12
= 12 – 6 + 5/12 = 11/12 work
So, 11/12 work will be done by A in (11/12 X 8) days
= 22/3 days = 7 1/3 days

Submit
24. A can complete a given task in 24 days, while B is twice as efficient as he. A started on the work initially, and was joined by B after a few days. If the whole work was completed in 10 days, after how many days, from the time A started working, did B join A?

Explanation

A can complete the work in 24 days
Efficiency of B is twice that of A
∴ B can complete the work in 24 X ½ = 12 days
According to the question, the work is completed in 10 days.
LCM of 24 and 12 = 24 units
Let the total work be 24 units
∴ A can do in one day 24/24 = 1 unit
A and B can do in one day = 24/12 = 2 units
Now, A works for 10 days
∴ Total work done by A in 10 days = 10 X 1 = 10 units’
∴ Remaining work = 24 – 10 = 14 units
Now, 14 units of work is done by B in 14/2 = 7 days
Hence B joined the work after (10 – 7) = 3 days.

Submit
25. 2 boys and 3 girls can do a piece of work in 8 days while 3 boys and 2 girls can do the same piece of work in 7 days. How much time will be taken by 5 boys and 4 girls to do the same piece of work?

Explanation

According to the question,
2b + 3g = 1/8
3b + 2g = 1/7
After solving both the equations,
We have b = 1/28 and g = 1/56
5b + 4g = 5/28 + 4/56 = 14/56 = 1/4
So, 5 boys and 4 girls can finish the work in 4 days.

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