Time and Work Mcqs MCQs

C takes 6 days to complete half of a work and D takes 5 days to complete 1/3rd of the same work. They take turns to complete the task. If C works for the first 4 days, in how many days will D complete the rest of the work without the help of C?

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A. 10 days
B. 12 days
C. 8 days
D. 9 days
✅ The correct answer is option A. 10 days.
Part of work completed by C in 1 day = 1/12 Part of work completed by D in 1 day = 1/15 Part of work completed by C in 4 days

= 1/3 Work remaining = 2/3 Time taken by D to complete the work

= (2/3)÷(1/15) = 10 days

A and B can do a work in 8 days, 13, 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_________?

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A. 4 days
B. 6 days
C. 8 days
D. 12 days
✅ The correct answer is option C. 8 days.
(A + B + C)’s 1 day’s work = 1/6; (A + B)’s 1 day’s work = 1/8 (B + C)’s 1 day’s work = 1/12 (A + C)’s 1 day’s work = ( 2 X 1/6 ) – ( 1/8 + 1/12 ) = ( 1/3 – 5/24 ) = 3/24 = 1/8 So, A and C together will do the woirk in 8 days.

8 children and 12 men complete a certain piece of work in 9 days. If 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 ?

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A. 6 days
B. 8 days
C. 10 days
D. 12 days
✅ The correct answer is option D. 12 days.
2 children = 1 man

(8 children + 12 men ) = 16 men

Now, less men, more days

12 : 16 : 9 : x

x = 16×9/12=12 days

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last ?

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A. 6 days
B. 10 days
C. 15 days
D. 20 days
✅ The correct answer is option B. 10 days.
Work done by X in 4 days = ( 1/20X 4 ) = 1/5 Remaining work = (1 – 1/5 ) = 4/5 (X + Y)’s 1 day’s work = 1/20 + 1/12 = 8/60 = 2/15 Now, 2/15 work is done by X and Y in 1 day. So, 4/5 work will be done by X and Y in 15/2 X 4/5 = 6 days Hence, total time taken = (6 + 4) days = 10 days.

A can do a certain work-in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in_________?

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A. 15 days
B. 20 days
C. 25 days
D. 30 days
✅ The correct answer is option C. 25 days.
(A + B)’s 1 day’s work = 1/10; C’s 1 day’s work = 1/50 (A + B + C)’s 1 day’s work = 1/10 + 1/50 = 6/50 = 3/25 Also, A’s 1 day’s work = (B + C)’s 1 day’s work

From (i) and (ii), we get : 2 x (A’s 1 day’s work) = 3/25 As 1 day’s work = 3/50 B’s 1 day’s work = 1/10 – 3/50 = 2/50 = 1/25 So, B alone could do the work in 25 days.

3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?

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A. 50
B. 30
C. 40
D. 13
✅ The correct answer is option C. 40.
Work done by 4 men and 6 women in 1 day = 1/8

Work done by 3 men and 7 women in 1 day = 1/10

Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as

4m + 6w = 1/8 —(1)

3m + 7w = 1/10 —(2)

Solving equation (1) and (2) , we get m=11/400 and w=1/400

Amount of work 10 women can do in a day = 10 × (1/400) = 1/40

Ie, 10 women can complete the work in 40 days

If 28 men can finish a work in 15 days, 21 men can finish the same work in___________?

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A. 24 days
B. 14 days
C. 15 days
D. 20 days
✅ The correct answer is option D. 20 days.
Time and Men are inversely proportional. Time taken by 28 men to finish the work = 15 days Time taken by a man to finish the work

= 15*28 days Time taken by 21 men = (15*28)/21 = 20 days

A is thrice as good a work man as B and takes 10 days less to do a piece of work than B takes. B can do the work in:___________?

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A. 15 days
B. 14 days
C. 16 days
D. 30 days
✅ The correct answer is option A. 15 days.
Raio of times taken by A and B = 1 : 3

If the difference of time is 2 days, B takes 3 days. If the difference of time is 10 days.

B takes [3/2×10]=15 days