Time and Work
- A, B and C individually can do a work in 10 days, 12 days and 15 days respectively. If they start working together, then the number of days required to finish the work is
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Work done by A, B and C in 1 day = 1 + 1 + 1 10 12 15 Work done by A, B and C in 1 day = 6 + 5 + 4 60 Work done by A, B and C in 1 day = 15 = 1 60 4
∴ Required time = 4 days
Second method to solve this question ,
Here , x = 10 , y = 12 , z = 15
Correct Option: C
Work done by A, B and C in 1 day = 1 + 1 + 1 10 12 15 Work done by A, B and C in 1 day = 6 + 5 + 4 60 Work done by A, B and C in 1 day = 15 = 1 60 4
∴ Required time = 4 days
Second method to solve this question ,
Here , x = 10 , y = 12 , z = 15Time Taken = xyz xy + yz + zx Time Taken = 10 × 12 × 15 10 × 12 + 12 × 15 + 15 × 10 Time Taken = 1800 120 + 180 + 150 Time Taken = 1800 = 4 days 450
- A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. A alone can finish the work in
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A’s 1 day’s work = 1 - 1 12 30 A’s 1 day’s work = 5 - 2 60 A’s 1 day’s work = 3 = 1 60 20
Hence, A alone will complete the work in 20 days.
Second method to solve this question ,
Here , x = 12 , y = 30
Time taken By A = xy x - y
Correct Option: A
A’s 1 day’s work = 1 - 1 12 30 A’s 1 day’s work = 5 - 2 60 A’s 1 day’s work = 3 = 1 60 20
Hence, A alone will complete the work in 20 days.
Second method to solve this question ,
Here , x = 12 , y = 30
Time taken By A = xy x - y Time taken By A = 12 × 30 30 - 12 Time taken By A = 12 × 30 = 20 days 18
- A, B and C can complete a piece of work in 12, 24 and 36 days respectively. In how many days will they together complete the same work ?
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(A + B + C)’s 1 day’s work = 1 + 1 + 1 12 24 36 (A + B + C)’s 1 day’s work = 6 + 3 + 2 = 11 72 72 ∴ (A + B + C) together will complete the work in 72 days 11 ∴ (A + B + C) together will complete the work in = 6 6 days 11
Second method to solve this question ,
Here , x = 12 , y = 24 , z = 36Time taken = xyz xy + yz + zx
Correct Option: C
(A + B + C)’s 1 day’s work = 1 + 1 + 1 12 24 36 (A + B + C)’s 1 day’s work = 6 + 3 + 2 = 11 72 72 ∴ (A + B + C) together will complete the work in 72 days 11 ∴ (A + B + C) together will complete the work in = 6 6 days 11
Second method to solve this question ,
Here , x = 12 , y = 24 , z = 36Time taken = xyz xy + yz + zx Time taken = 12 × 24 × 36 12 × 24 + 24 × 36 + 12 × 36 Time taken = 24 × 36 24 + 72 + 36 Time taken = 24 × 36 132 = 72 days 11 Time taken = 6 6 days 11
- A and B can separately do a piece of work in 6 days and 12 days respectively. How long will they together take to do the work ?
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(A + B)’s 1 day’s work = 1 + 1 6 12 (A + B)’s 1 day’s work = 2 + 1 = 1 12 4
∴ A and B together will complete the work in 4 days.
Second method to solve this question ,
Here , x = 6 , y = 12
Correct Option: D
(A + B)’s 1 day’s work = 1 + 1 6 12 (A + B)’s 1 day’s work = 2 + 1 = 1 12 4
∴ A and B together will complete the work in 4 days.
Second method to solve this question ,
Here , x = 6 , y = 12Time taken = x × y x + y Time taken = 6 × 12 6 + 12 Time taken = 72 = 4 days 18
- A and B can do a piece of work in 6 days and A alone can do it in 9 days. The time taken by B alone to do the same work is ?
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B's one day's work = (1/6 - 1/9) = 1/18
Correct Option: A
B's one day's work = (1/6 - 1/9) = 1/18
∴ B alone can finish it in 18 days.
