Time and Work
- A can complete a job in 9 days, B in 10 days and C in 15 days. B and C start the work and are forced to leave after 2 days. The time taken to complete the remaining work is ?
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(B + C)'s 2 day's work = 2 x (1/10 + 1/15) = 1/3
Remaining work = (1 - 1/3) = 2/3
∵ 1/9 work is done by A in 1 day
∴ 2/3 work is done by A in (9 x 2) / 3 = 6 daysCorrect Option: A
(B + C)'s 2 day's work = 2 x (1/10 + 1/15) = 1/3
Remaining work = (1 - 1/3) = 2/3
∵ 1/9 work is done by A in 1 day
∴ 2/3 work is done by A in (9 x 2) / 3 = 6 days
- Twelve men can complete a work in 8 days. Three days after they started the work, 3 more men joined them. In how, many days will all of them together complete the remaining work
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1 men's one day's work = 1/96
12 men's 3 day's work = 3 x (1/8) = 3/8
Remaining work = (1 - 3/8) = 5/8
15 men's 1 day's work = 15/96
Now, 15/96 work is done by them in 1 day
∴ 5/8 work will be done by them in = (96/15) x (5/ 8) i.e., 4 daysCorrect Option: B
1 men's one day's work = 1/96
12 men's 3 day's work = 3 x (1/8) = 3/8
Remaining work = (1 - 3/8) = 5/8
15 men's 1 day's work = 15/96
Now, 15/96 work is done by them in 1 day
∴ 5/8 work will be done by them in = (96/15) x (5/ 8) i.e., 4 days
- A can do a piece of work in 10 days and B can do the same piece of work in 20 days. They start the work together but after 5 days A leaves off, B will do the remaining piece of work in ?
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(A + B)'s 5 day's work = 5 x (1/10 + 1/20) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/20 work is done by B in = 1 dayCorrect Option: A
(A + B)'s 5 day's work = 5 x (1/10 + 1/20) = 3/4
Remaining work = (1 - 3/4) = 1/4
1/20 work is done by B in = 1 day
∴ 1/4 work is done by B in = 20 x (1/4) i.e., 5 days.
- A completes a work in 15 days. B complete the same work in 20 days. A started working alone after 1 days B joined him. How many day will they now take together to complete the remaining work ?
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Work of A for 1 day = 1/15
Work of B for 1 day = 1/20
Work of (A + B) together for 1 day = 1/15 + 1/20 = (4 + 3)/60 = 7/60
Remaining work after A alone does for 1 day = 1 - 1/15 = 14/15
∵ 7/60 part-work can be complete by (A + B) in 1 days
∴ 14/15 part-work can be completed by (A + B) in = (60/7) x (14/15) = 8 days.Correct Option: A
Work of A for 1 day = 1/15
Work of B for 1 day = 1/20
Work of (A + B) together for 1 day = 1/15 + 1/20 = (4 + 3)/60 = 7/60
Remaining work after A alone does for 1 day = 1 - 1/15 = 14/15
∵ 7/60 part-work can be complete by (A + B) in 1 days
∴ 14/15 part-work can be completed by (A + B) in = (60/7) x (14/15) = 8 days.
- A can do a piece of work in 12 days, B can do the same work in 8 days and c can do the same job in 4 / 5 th time required by both A and B. A and B work together for 3 days, then C complete days did C work ?
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As per question, work of A for 1 day = 1/12 and work of B for 1 day = 1/8
∴ Work of (A + B) together for 1 day = 1/12 + 1/8 = (2 + 3)/24 = 5/24
⇒ Work of (A + B) together for 3 days = 3 x (5/24) = 5/8
⇒ Remaining work after 3 days = 1 - 5/8 = 3/8
∵ C can do the same work in = 4/5th time required by (A + B) = 4/5 x 24/5 = 96/25 days
⇒ Work of C for 1 day = 25/96 part.
⇒ 25/96 part work can be done by C in 1 day
⇒ 3/8 part work can be done by C in = 96/25 x 3/8 days = 36/25 days = 111/25
∴ The complete day C did the work = 1 day.Correct Option: D
As per question, work of A for 1 day = 1/12 and work of B for 1 day = 1/8
∴ Work of (A + B) together for 1 day = 1/12 + 1/8 = (2 + 3)/24 = 5/24
⇒ Work of (A + B) together for 3 days = 3 x (5/24) = 5/8
⇒ Remaining work after 3 days = 1 - 5/8 = 3/8
∵ C can do the same work in = 4/5th time required by (A + B) = 4/5 x 24/5 = 96/25 days
⇒ Work of C for 1 day = 25/96 part.
⇒ 25/96 part work can be done by C in 1 day
⇒ 3/8 part work can be done by C in = 96/25 x 3/8 days = 36/25 days = 111/25
∴ The complete day C did the work = 1 day.
