Time and Work
- A does half as much work as B in one sixth of the time. If together they take 10 days to complete a work, how much time shall B take to do it alone?
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Let B does the whole work in x days
∴ Work done by B in 1 day 1 x
According to questionA does the 1 work in x days 2 6 ∴ A does the whole work in 2x 6 or = x days 3 ∴ Work done by A in one day = 3 x
∴ Work done by A and B together in one day= 1 + 3 = 4 x x x
∴ Time taken to complete the whole work by A and B together= 1 = x days 4/x 4
Again, given thatx = 10 4
∴ x = 40 days
Aliter : Using Rule 22,
Here, n = 3, d = 10
∵ A is 3 times more efficient thanB.
Time taken by B = (n + 1) × D
= (3 + 1) × 10
= 40 daysCorrect Option: C
Let B does the whole work in x days
∴ Work done by B in 1 day 1 x
According to questionA does the 1 work in x days 2 6 ∴ A does the whole work in 2x 6 or = x days 3 ∴ Work done by A in one day = 3 x
∴ Work done by A and B together in one day= 1 + 3 = 4 x x x
∴ Time taken to complete the whole work by A and B together= 1 = x days 4/x 4
Again, given thatx = 10 4
∴ x = 40 days
Aliter : Using Rule 22,
Here, n = 3, d = 10
∵ A is 3 times more efficient thanB.
Time taken by B = (n + 1) × D
= (3 + 1) × 10
= 40 days
- P can do 1/4 th of work in 10 days, Q can do 40% of work in 40 days and R can do 1/3 rd of work in 13 days. Who will complete the work first?
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∵ P does 1/4 th work in 10 days.
∴ P will do 1 work in 10 × 4 = 40 days
∵ Q, does 40% part of work in 40 days
∴ Q will do 100% work in40 × 100 = 100 days 40 ∵ R, does 1 rd work in 13 days. 3
∴ R will do 1 work in 13 × 3 = 39 daysCorrect Option: C
∵ P does 1/4 th work in 10 days.
∴ P will do 1 work in 10 × 4 = 40 days
∵ Q, does 40% part of work in 40 days
∴ Q will do 100% work in40 × 100 = 100 days 40 ∵ R, does 1 rd work in 13 days. 3
∴ R will do 1 work in 13 × 3 = 39 days
- A, B and C contract a work for Rs. 440. A and B together are to do 9 /11 of the work. The share of C should be :
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Work done by A and B together
= 9 parts 11
∴ Work done by C= 1 - 9 = 2 parts 11 11
Total amount = Rs. 440∴ C’s share = Rs. 
2 × 440 
= Rs. 80 11 Correct Option: D
Work done by A and B together
= 9 parts 11
∴ Work done by C= 1 - 9 = 2 parts 11 11
Total amount = Rs. 440∴ C’s share = Rs. 2 × 440 = Rs. 80 11
- A can do 1/3 rd of a work in 5 days and B can do 2/5 th of this work in 10 days. Both A and B, together can do the work in
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∵ A does 1/3 rd part of work in 5 days.
∴ A will do 1 work in 5 × 3 = 15 days.
∵ B does 2/5 th of work in 10 days∴ B will do 1 work in 10 × 5 = 25 days. 2
∴ (A + B)’s 1 day’s work= 1 + 1 15 25 = 5 + 3 = 8 75 75 ∴ Required time = 75 = 9 3 8 8 Correct Option: C
∵ A does 1/3 rd part of work in 5 days.
∴ A will do 1 work in 5 × 3 = 15 days.
∵ B does 2/5 th of work in 10 days∴ B will do 1 work in 10 × 5 = 25 days. 2
∴ (A + B)’s 1 day’s work= 1 + 1 15 25 = 5 + 3 = 8 75 75 ∴ Required time = 75 = 9 3 8 8
- A and B together can complete a work in 24 days. B alone does 1/3 rd part of this work in 12 days. How many days will A alone take to complete the remaining work?
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∵ B completes 1 work in 12 days. 3
∴ B will complete 1 work in 12 × 3 = 36 days.∴ B’s 1 day’s work = 1 36 (A + B)’s 1 day’s work = 1 24 ∴ A’s 1 day’s work = 1 - 1 24 36 = 3 - 2 = 1 72 72
∴ Time taken by A in doing 1 work = 72 daysRemaining work = 1 – 1 = 2 3 3
∴ Time taken by A in doing2 work = 2 × 72 = 48 days 3 3 Correct Option: C
∵ B completes 1 work in 12 days. 3
∴ B will complete 1 work in 12 × 3 = 36 days.∴ B’s 1 day’s work = 1 36 (A + B)’s 1 day’s work = 1 24 ∴ A’s 1 day’s work = 1 - 1 24 36 = 3 - 2 = 1 72 72
∴ Time taken by A in doing 1 work = 72 daysRemaining work = 1 – 1 = 2 3 3
∴ Time taken by A in doing2 work = 2 × 72 = 48 days 3 3
