Time and Work
- A, B and C can do a job in 6 days, 12 days and 15 days re spectively. After 1/8 of the work is completed, C leaves the job. Rest of the work is done by A and B together. Time taken to finish the work is
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Remaining work
= 1 – 1 = 7 8 8
(A + B)’s 1 day’s work= 1 + 7 6 12 = 2 + 1 = 3 = 1 12 12 4 ∴ Time taken in doing 7 part of work 8 = 7 × 4 = 7 8 2 = 3 1 days. 2 Correct Option: C
Remaining work
= 1 – 1 = 7 8 8
(A + B)’s 1 day’s work= 1 + 7 6 12 = 2 + 1 = 3 = 1 12 12 4 ∴ Time taken in doing 7 part of work 8 = 7 × 4 = 7 8 2 = 3 1 days. 2
- A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days.A alone can finish the work in
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(A + B) together do the work in 30 days.
∴ (A + B)’s 1 day’s work = 1 30
∴ (A + B)’s 20 days’ work= 20 = 2 30 3 Remaining work = 1 – 2 = 1 3 3 ∵ Time taken by A in doing 1 work = 20 days 3
∴ Time taken in doing 1 work
= 20 × 3 = 60 days.
Aliter : Using Rule 9,
Here, a = 30, b = 20, d = 20
A alone can finish the work in= ad days a - b = 30 × 20 = 60 days 30 - 20 Correct Option: A
(A + B) together do the work in 30 days.
∴ (A + B)’s 1 day’s work = 1 30
∴ (A + B)’s 20 days’ work= 20 = 2 30 3 Remaining work = 1 – 2 = 1 3 3 ∵ Time taken by A in doing 1 work = 20 days 3
∴ Time taken in doing 1 work
= 20 × 3 = 60 days.
Aliter : Using Rule 9,
Here, a = 30, b = 20, d = 20
A alone can finish the work in= ad days a - b = 30 × 20 = 60 days 30 - 20
- A and B together can complete a job in 8 days. Both B and C, working alone can finish the same job in 12 days. A and B commence work on the job, and work for 4 days, where upon A leaves. B continues for 2 more days, and then he leaves too. C now starts working, and finishes the job. How many days did C require ?
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Work done by A and B in first 6 days
= (A + B)’s 4 days’ work + B’s 2 days’ work= 4 × 1 + 1 8 12 = 1 + 1 2 6 = 3 + 1 = 4 = 2 6 6 3
Remaining work= 1 - 3 = 1 3 3
∴ Time taken by C= 1 × 12 = 4 days. 3 Correct Option: D
Work done by A and B in first 6 days
= (A + B)’s 4 days’ work + B’s 2 days’ work= 4 × 1 + 1 8 12 = 1 + 1 2 6 = 3 + 1 = 4 = 2 6 6 3
Remaining work= 1 - 3 = 1 3 3
∴ Time taken by C= 1 × 12 = 4 days. 3
- A can do in one day three times the work done by B in one day. They together finish 2/5 of the work in 9 days. The number of days by which B can do the work alone is :
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Let time taken by A alone in doing work be x days.
∴ Time taken by B alone = 3x days∵ A and B together finish 2 work in 9 days. 5
∴ TIme taken by A and B in doing whole work= 9 × 5 = 45 days 2 2 = 1 + 1 = 2 x 3x 45 ⇒ 3 + 1 = 2 3x 45 ⇒ 4 = 2 ⇒ 2 × 3x = 4 × 45 3x 45 ⇒ x = 4 × 45 = 30 days 2 × 3
∴ Time taken by B = 3x days = 3 × 30 = 90 days
Aliter : Using Rule 22,
Here, n = 3 and D= 9 × 5 = 45 days 2 2
(Time taken to finish whole work)
Time taken by B = (n + 1)D= (3 + 1) × 45 = 90 days 2 Correct Option: A
Let time taken by A alone in doing work be x days.
∴ Time taken by B alone = 3x days∵ A and B together finish 2 work in 9 days. 5
∴ TIme taken by A and B in doing whole work= 9 × 5 = 45 days 2 2 = 1 + 1 = 2 x 3x 45 ⇒ 3 + 1 = 2 3x 45 ⇒ 4 = 2 ⇒ 2 × 3x = 4 × 45 3x 45 ⇒ x = 4 × 45 = 30 days 2 × 3
∴ Time taken by B = 3x days = 3 × 30 = 90 days
Aliter : Using Rule 22,
Here, n = 3 and D= 9 × 5 = 45 days 2 2
(Time taken to finish whole work)
Time taken by B = (n + 1)D= (3 + 1) × 45 = 90 days 2
- Babu and Asha can do a job together in 7 days.
Asha is 1 3 times 4
as efficient as Babu. The same job can be done by Asha alone in
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Ratio of efficiency of Babu and Asha
= 1 : 7 = 4 : 7 4
As the time taken is inversely proportional to efficiency, therefore, if Babu takes 7x days to complete work, Asha will take 4x days.= 1 + 1 = 1 7x 4x 7 ⇒ 4 + 7 = 1 28x 7
⇒ 28x = 11 × 7⇒ x = 11 × 7 = 11 28 4
∴ Asha will complete the work in4x = 4 × 11 = 11 days 4
Aliter : Using Rule 22,Here, n = 7 , D = 7 4
∴ Time taken by Asha= 
n + 1 
× D days n = (7/4) + 1 × 7 7/4 = 11 × 7 = 11 days 4 Correct Option: C
Ratio of efficiency of Babu and Asha
= 1 : 7 = 4 : 7 4
As the time taken is inversely proportional to efficiency, therefore, if Babu takes 7x days to complete work, Asha will take 4x days.= 1 + 1 = 1 7x 4x 7 ⇒ 4 + 7 = 1 28x 7
⇒ 28x = 11 × 7⇒ x = 11 × 7 = 11 28 4
∴ Asha will complete the work in4x = 4 × 11 = 11 days 4
Aliter : Using Rule 22,Here, n = 7 , D = 7 4
∴ Time taken by Asha= n + 1 × D days n = (7/4) + 1 × 7 7/4 = 11 × 7 = 11 days 4
