Time and Work :(96) MCQs with Answers
1.
A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be
Answer: Option 'A'
If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 12 × 24/ 36 = 8 days.
2.
If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
Answer: Option 'A'
The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
3.
If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in
Answer: Option 'D'
That is, 1 person can do one time of the work in 3 days.
Therefore, 7 persons can do 7 times work in the same 3 days itself.
4.
Mangala completes a piece of work in 10 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is
Answer: Option 'D'
If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 10 × 40/50 = 8 days.
5.
12 men work 8 hours per day to complete the work in 10 days. To complete the same work in 8 days, working 15 hours a day, the number of men required
Answer: Option 'D'
That is, 1 work done = 12 × 8 × 10
Then, 12 8 × 10 = ? × 15 × 8
? (i.e. No. of men required) = 12 × 8 × 10/15× 10 = 8 days.
6.
If 5 people undertook a piece of construction work and finished half the job in 15 days. If two people drop out, then the job will be completed in
Answer: Option 'A'
That is, half the work done = 5 × 15 × ½
Then, 5 × 15 × ½ = 3 × ? ×1/2
i.e. 5 × 15 = 3 × ?
therefore, ? (No. days required) = 5 × 15/3 = 25 days.
7.
30 labourers working 7 hours a day can finish a piece of work in 18 days. If the labourers work 6 hours a day, then the number of labourers required to finish the same piece of work in 30 days will be
Answer: Option 'B'
That is, 1 work done = 30 × 7 ×18 = ? × 6 × 30
? (No. of labourers) = 30 × 7 × 18/6 × 30 = 21
8.
If 5 girls can embroider a dress in 9 days, then the number of days taken by 3 girls will be
Answer: Option 'D'
That is, 5 × 9 = 3 × ?
? = 5 × 9/3 = 15 days
9.
A and B together can plough a field in 10 hours but by himself A requires 15 hours. How long would B take to plough the same field?
Answer: Option 'C'
If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.
Therefore, the No. of hours required by B = 10 × 15/ 15 – 10 = 150/5 = 30 hours.
10.
16 men or 20 women can finish a work in 25 days. How many days 28 men and 15 women will take to finish this job?
Answer: Option 'D'
16 men = 20 women
Therefore, 1 women = 16/20 men = 4/5 men
15 women = 4/5 × 15 men = 12 men
i.e. 28 men + 15 women = 28 men + 12 men = 40men
1 work done by men = 16 × 25
16 × 25 = 40 × ?
? ( no. of days) = 16 × 25/40 = 10 days.
11.
A can do a piece of work in 5 days and B can do the same work in 10 days. How many days will both take to complete the work?
Answer: Option 'B'
If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 5 × 10/15 = 3 1/3 days.
12.
If 12 men can do a piece of work in 24 days, then in how many days can 18 men do the same work?
Answer: Option 'D'
1 work done = 12 × 24
Then, 12 × 24 = 18 × ? days
? days = 12 × 24/18 = 16.
13.
A group of workers accepted to do a piece of work in 25 days. If 6 of them did not turn for the work and the remaining workers did the work in 40 days, then the original number of workers was
Answer: Option 'D'
Let the original number of workers be ‘x’
Then, x × 25 = (x – 6) × 40
25x = 40x -240
240 = 40x -25x = 15x
x = 240/15 = 16.
14.
If 8 men or 12 women can do a piece of work in 10 days, then the number of days required by 4 men and 4 women to finish the work is
Answer: Option 'C'
8 men = 12 women
1 woman = 8/12 men = 2/3 men
4 women = 2/3 × 4 men = 8/3 men
4 men + 4 women = 4 + 8/3 men = 20/3 men
1 work done = 8 × 10
8 × 10 = 20/3 × ?days
? days = 8 × 10 × 3/20 = 12 days.
15.
If 8 men can dig a well in 18 days, then the number of days, 12 men will take to dig the same well will be
Answer: Option 'A'
Work done = 8 × 18
Then, 8 × 18 = 12 × ? days
? days = 8 × 18/12 = 12 days
16.
39 men can repair a road in 12 days working 5 hours a day. In how many days will 30 men working 6 hours peer day complete the work?
Answer: Option 'B'
1 work done = 39 × 12 × 5
39 × 12 × 5 = 30 × 6 × ? days
? days = 39 × 12 × 5/ 30 × 6 = 13 days.
17.
A certain number of men can do a work in 40days. If there were 8 men more, it could be finished in 10 days less. How many men were there initially?
Answer: Option 'B'
Let ‘x’ be the initial number of men
Then, 1 work done = x × 40
Then, x × 40 = (x + 8 ) (40 – 10)
40x = 30x + 240
10x = 240
Therefore, x = 240/10 = 24 men.
18.
If 4 men or 6 boys can finish a work in 20 days. How long will 6 men and 11 boys take to finish the same work?
Answer: Option 'B'
4 men = 6 boys
Then, 1 boy = 4/6 men = 2/3 men
11 boys = 2/3 × 11 men = 22/3 men
Then, 6 men + 11 boys = 6 + 22/3 men = 40/3 men
1 work done = 4 men × 20days
That is, 4 × 20 = 40/3 × ? days
? days = 4 × 20 × 3/40 = 6 days
19.
A works twice as fast as B. if B can complete a work in 12 days independently. The number of days in which A and B can together finish the work?
Answer: Option 'D'
If B takes 12 days to finish the work, then A takes 6 days to finish the same work.
If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.
Therefore, the Number of days taken by A and B together to finish the same work = 6 × 12/18
= 4 days.
20.
A and B can do a piece of work in 4 days. If A can do it alone in 12 days, B will finish the work in
Answer: Option 'B'
If A and B together can do a piece of work in x days and A alone can do the same work in y
days, then B alone can do the same work in x y/ y – x days.
Therefore, the number of days B will take to finish the work = 4 × 12/ 12 – 4
= 48/8 = 6 days.
21.
5 men can do a piece of work in 6 days while 10 women can do it in 5 days. In how many days can 5 women and 3 men do it?
Answer: Option 'B'
5men × 6 = 10 women × 5
30 men = 50 women
1 woman = 30/50 men = 3/5 men
5 women = 3/5 × 5 men = 3 men
5 women + 3 men = 3 + 3 = 6 men
That is, 1 work done = 5 × 6
5 × 6 = 6 × ?days
? days = 5 × 6/6 = 5 days.
22.
A work could be completed in 100 days. However, due to the absence of 10 workers, it was completed in 110 days then, the original number of workers was
Answer: Option 'B'
Let ‘x’ be the original number of workers
Then, x × 100 = ( x – 10) 110
100 x = 110x – 1100
1100 = 10 x
x = 110.
23.
A particular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to completed the job if the two teams work together?
Answer: Option 'A'
Consider men’s work days as one group and women’s working days as other group Then, the required No. of days = 12 × 6/18 = 4 days.
24.
A can do a piece of work in 12 days, while B can do it in 8 days with the help of C, they finish the work in 4 days. Then C alone can do the work in
Answer: Option 'A'
A and B together can do the work in 12 × 8/20 = 96/20 days
A +B and C together do the work in 4 days.
Then C alone can do the work in 96/20 × 4/96/20 – 4 days
= 96/5/16/20 = 96/5 × 20/16 = 24 days.
25.
A job can be completed by 12 men in 12 days. How many extra days will be needed to complete the job if 6 men leave after working for 6 days?
Answer: Option 'D'
Half the work is done by 12 men in 6 days.
Remaining half should be done by 6 men in ? days
Then, 12 × 6 × ½ = 6 × ?days × ½
36 = 3 × ?days
? days = 36/3 =12 days
Extra days required = 12 -6 = 6 days.
26.
Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take, worker A and worker B, working together but independently, do the same job?
Answer: Option 'C'
If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.
Then 8 × 10/18 = 4 4/9 hours.
27.
Three workers working all days can do a work in 10 days. But one of them having other employment can work only half time. In how many days the work can be finished?
Answer: Option 'D'
Sum of each persons’ one day’s work = 1/3 ×10 + 1/3 ×10 + 1/3× 20 = 1/30 + 1/30 + 1/60
= 5/60 = 1/12
Therefore, the work can be finished in 12 days.
28.
Sam, Bob and Kim can do a job alone in 15 days, 10 days and 30 days respectively. Sam is helped by Bob and Kim every third day. In how many days will the job be completed?
Answer: Option 'A'
The work done by the three persons in 3 days ( because Sam works only on every third day)
= 3/15 + 1/10 + 1/30 = 6 + 3 + 1/30 = 10/30
= 1/3 of the work
Therefore, the job will be completed in 3 × 3 = 9 days.
29.
Prakash alone can complete a job in 12 hours, Jayant alone can complete the same job in 6 hours. How many hours will they take together to complete the job?
Answer: Option 'A'
If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.
Here, the No. of hours required to complete the work , working together = 12 × 6/18
= 4 hours.
30.
56 men completes a work in 12 days. How many men will be required to complete the work in 16 days?
Answer: Option 'C'
1 work done = 56 men × 12 days
Then, 56 ×12 = ? men × 16
? men = 56 × 12/16 = 42 men.
31.
Six men or tern boys can do a piece of work in fifteen days. How long would it take for 12 men and 5 boys to do the same piece of work?
Answer: Option 'A'
6 men = 10 boys
Then, 1 boy = 6/10 men = 3/5 men
Then, 5 boys = 3/5 × 5 = 3 men
12 men + 5 boys = 15 men
1 work done = 6 men × 15 days
Therefore, 6 × 15 = 15 × ? days
? days = 6 × 15/15 = 6 days.
32.
If 4 workers can make 42 toys in 6 days, how many toys can 12 workers make in 3 days?
Answer: Option 'A'
4 workers in 3 days make 21 toys,
Then, 1 worker can make 21/4 toys in 3 days
Therefore, No. of toys made by 12 workers in 3 days = 21/4 × 12 = 63 toys.
33.
10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will work get completed?
Answer: Option 'C'
If A can complete a work in x days and B can complete the same work in y days,
then, both of them together can complete the work in x y/ x+ y days.
Here, men’s working days can be taken as A and that of women as B
Then, 15 × 12/27 = 6 2/3 days.
34.
Three men, four women and six children can complete a work in 7 days . A woman does double the work a man does and a child does half the work a man does. How many women can complete this work in 7 days?
Answer: Option 'B'
3 men = 3/2 women
1 child = 1/2/2 = ¼ woman
Then, 6 children = ¼ × 6 = 6/4 = 3/2 women
Then, 3/2 women + 4 women + 3/2 women = 7 women
7 women does the work in 7 days.
Therefore, the No. of women required to finish the work in 7days = 7.
35.
A sum of money is sufficient to pay P’s wages for 25 days or Q’s wages for 30 days. The money is sufficient to pay the wages of both for
Answer: Option 'D'
If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.
Here, wages can be taken as days,
Then, 25 ×30/ 55 = 13 7/11 days.
36.
A certain number of men complete a piece of work in 50 days. If there were 8 men more the work could be finished in 10 days less. How many men were originally there?
Answer: Option 'C'
Let the original No. of men = x
Then, I work done = 50x
Then, 50x = (x + 8) 40 50x = 40x + 320
10 x = 320
x = 320/10 = 32 men.
37.
A and B together finish a work in 30 days they worked for it for 20 days and then B left. The remaining work was done by A alone in 20 more days. B alone can finish the work in
Answer: Option 'D'
(A + B)’s 1 days work = 1/30
A+B ‘s 20 days work = 1/30 × 20 = 2/3
Remaining work = 1 -2/3 = 1/3
1/3 of the work is done by A in 20 days
Therefore, A can complete the full work in 3 × 20 = 60 days
So, A’s 1 day’s work = 1/60
Then, B’s 1 day work = 1/30 – 1/60 = 1/60
Therefore, B can complete the work in 60 days.
38.
A can complete a job in 9 days, B in 10 days and C in 15 days. B and C start the work together and are forced to leave after 2 days. The time taken to complete the remaining work is
Answer: Option 'D'
A’s 1 day work = 1/9
B’s 1 day work = 1/10
C’s 1 day work = 1/15
B + C ‘ s 1 day work = 1/10 + 1/15 = 1/6
B + C’s 2 day’s work = 1/6 × 2 = 1/3
The work remaining = 1 – 1/3 = 2/3
A can do the full work in 9 days.
So, the remaining 2/3 of the work is done by A in 2/3 × 9 days = 6 days.
39.
If 40 men working 9 hours a day can finish a work in 21 days, in how many days will 27 men working 10 hours a day do the same work?
Answer: Option 'B'
That is, 1 work done = 40 × 9 × 21
Then, 40 × 9 × 21 = 27 × 10 × ? days
Therefore, ? days = 40 × 9 × 21 /27 × 10 = 28 days.
= 4 hours.
40.
8 children and 12 men complete a certain piece of work in 9 days. Each child takes twice the time taken by a man to finish the work. In how many days will 12 men finish the same work?
Answer: Option 'C'
8 children = 4men
Then, 4 + 12 = 16 men completes the job in 9 days
Then, 16 × 9 = 12 × ? days
? days = 16 × 9/12 = 12 days.
41.
Rajesh and Ajay can complete a job in 16 days. Rajesh alone can do it in 24 days. How long will Ajay alone take to finish the whole work?
Answer: Option 'B'
If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.
Then, Ajay alone can finish the whole work in, 16 × 24/24 – 16 = 16 × 24/8 = 48 days.
42.
Ram, Shyam and Mohan can do a piece of work in 12, 15 and 20 days respectively. How long will they take to finish it together?
Answer: Option 'D'
When A, B and C can do a work in x, y and z days respectively. Then, the three of them together can finish the work in xyz/ x y + y z + x z days
Therefore, the No. of days taken by them together to finish the whole work
= 12 × 15 × 20/12 × 15 + 15 × 20 + 12 × 20
= 12 × 15 × 20/720 = 5 days.
43.
Tapas works twice as much as Mihir. If both of them finish the work in 12 days, Tapas alone can do it in:
Answer: Option 'C'
Mihir = 2 Tapas (Consider, Tapas as ‘T’ and Mihir as “M”)
So, T ×2 T/ T + 2T = 12
2 T × T/3 T = 12
2 T = 3 × 12 = 36
T = 36/2 = 18 days i.e. No. of days taken by Tapas alone = 18 days.
44.
Xavier can do a job in 40 days. He worked on it for 5 days and then Paes finished it in 21 days. In how many days Xavier and Paes can finish the work?
Answer: Option 'B'
Xavier’s one day’s work = 1/40
His 5 days work = 1/40 × 5 = 1/8
The work remaining = 1 – 1/8 = 7/8
7/8 of the work is done by Paes in 21 days
Then, his 1 day’s work = 7/8/21 = 7/21 × 8 = 1/24
Therefore, the time taken by Paes to finish the whole work = 24 days.
Then. The No. of days two of them together take to finish the work = 40 × 24/40 + 24
= 40 × 24/64 = 15 days.
45.
A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?
Answer: Option 'A'
B alone can do the same work in 9 days
So, the No. of days both of them together take to do the work = 18 × 9/ 18 + 9
=18 × 9/27 = 6 days.
The part of the work, they together finish in one day = 1/6.
46.
A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
Answer: Option 'C'
When A, B and C can do a work in x, y and z days respectively. Then, the three of them
together can finish the work in xyz/ x y + y z + x z days
Therefore, the No. of days taken by them together = 24 × 6 × 12/24 × 6 + 6 × 12 + 24 × 12
= 24 × 6 × 12/ 504 = 3 3/7 days.
47.
A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone?
Answer: Option 'C'
If A and B together can do a piece of work in x days and A alone can do the same work in y days, then B alone can do the same work in x y/ y – x days.
Therefore, his son alone can do the work in 3 × 5/ 5 – 3 = 15/2 = 7 ½ days.
48.
A works twice as fast as B. if B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is:
Answer: Option 'A'
That is, if b alone can finish the work in 12 days,
A alone can finish the work in 6 days.
If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days.
A and B can together finish the work in 6 × 12/18 days = 4 days.
49.
A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is:
Answer: Option 'B'
A’s work is twice as B’s work
So, we can consider 2A = B
Then, A × 2A/ A+ 2A = 14
2A × A/ 3A = 14
2 A = 14 × 3
A = 21 days. i.e. A alone can finish the work in 21 days.
50.
A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
Answer: Option 'B'
That is, 3A = B, replacing 3 A in place of B, we get
3A – A = 60 days
A = 30 days, i.e. A alone can finish the work in 30 days
Then, B alone can finish the work in 3 ×30 = 90 days
Therefore, working together they can finish it in 30 × 90/ 120 days. = 22 ½ days. .
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