Time and Work
- A can do a work in 10 days and B in 20 days. If they together work on it for 5 days, then the fraction of the work that is left is
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Using basics of Rule 2
Work done by A and B in 1 day1 + 1 = 2 + 1 = 3 10 20 20 20
∴ (A + B)’s 5 days’ work= 5 × 3 = 3 20 4
∴ Remaining work= 1 - 3 = 1 4 4 Correct Option: D
Using basics of Rule 2
Work done by A and B in 1 day1 + 1 = 2 + 1 = 3 10 20 20 20
∴ (A + B)’s 5 days’ work= 5 × 3 = 3 20 4
∴ Remaining work= 1 - 3 = 1 4 4
- A, B and C are employed to do a piece of work for Rs. 5,290. A and B together are supposed to do 19/23 of the work and B and C together 8/23 of the work. Then A should be paid
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Part of work done by A and
B = 19 23
∴ Part of work done by C= 1 - 19 = 4 23 23
Part of work done by B and C= 8 23
∴ Part of work done by B= 8 - 4 = 4 23 23 23
∴ Part of work done by A= 19 - 4 = 15 23 23 23
∴ Ratio of the shares of wages of A, B and C= 15 : 4 : 4 = 15 : 4 : 4 23 23 23
∴ A’s share= 15 × 5290 = Rs. 3450 23 Correct Option: B
Part of work done by A and
B = 19 23
∴ Part of work done by C= 1 - 19 = 4 23 23
Part of work done by B and C= 8 23
∴ Part of work done by B= 8 - 4 = 4 23 23 23
∴ Part of work done by A= 19 - 4 = 15 23 23 23
∴ Ratio of the shares of wages of A, B and C= 15 : 4 : 4 = 15 : 4 : 4 23 23 23
∴ A’s share= 15 × 5290 = Rs. 3450 23
- A does half as much work as B in three fourth of the time. If together they take 18 days to complete the work, how much time will B alone take to do it ?
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Let the time taken by B in doing the work alone = x days
According to the question,
Time taken by A= 2 × 3x = 3x days 4 2 ∴ 1 + 1 = 1 x 3x 18 2 ⇒ 1 + 2 = 1 x 3x 18 ⇒ 3 + 2 = 1 3x 18
⇒ 3x = 18 × 5⇒ x = 18 × 5 = 30 days 3 Correct Option: D
Let the time taken by B in doing the work alone = x days
According to the question,
Time taken by A= 2 × 3x = 3x days 4 2 ∴ 1 + 1 = 1 x 3x 18 2 ⇒ 1 + 2 = 1 x 3x 18 ⇒ 3 + 2 = 1 3x 18
⇒ 3x = 18 × 5⇒ x = 18 × 5 = 30 days 3
- x does 1/4 of a job in 6 days. y completes rest of the job in 12 days. Then x and y could complete the job together in
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Using basics of Rule 2,
x does 1 work in 6 days 4
∴ x does 1 work in 24 days
Similarly,y does 3 work in12 days 4 ∴ y does 1 work in 12 × 4 = 16 days 3
(x + y)’s 1 day’s work1 + 1 = 2 + 3 = 5 24 16 48 48 ∴ Required time = 48 5 = 9 3 days 5 Correct Option: B
Using basics of Rule 2,
x does 1 work in 6 days 4
∴ x does 1 work in 24 days
Similarly,y does 3 work in12 days 4 ∴ y does 1 work in 12 × 4 = 16 days 3
(x + y)’s 1 day’s work1 + 1 = 2 + 3 = 5 24 16 48 48 ∴ Required time = 48 5 = 9 3 days 5
- A company employed 200 workers to complete a certain work in 150 days. If only one fourth of the work has been done in 50 days, then in order to complete the whole work in time, the number of additional workers to be employed was
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Using Rule 1,
200 workers do 1 work in 50 days. 4 How many workers will do 3 work in 100 days ? 4
Number of additional workers = x (let)∴ M1D1 = M2D2 W1 W2 ⇒ 200 × 50 1/4 = (200 + x) × 100 3/4
⇒ (200 + x) 100 = 3 × 200 × 50
⇒ 200 + x = 300
⇒ x = 300 – 200 = 100Correct Option: A
Using Rule 1,
200 workers do 1 work in 50 days. 4 How many workers will do 3 work in 100 days ? 4
Number of additional workers = x (let)∴ M1D1 = M2D2 W1 W2 ⇒ 200 × 50 1/4 = (200 + x) × 100 3/4
⇒ (200 + x) 100 = 3 × 200 × 50
⇒ 200 + x = 300
⇒ x = 300 – 200 = 100
