Time and Work
- A and B can do a job in 6 and 12 days respectively. They began the work together but A leaves after 3 days. Then the total number of days needed for the completion of the work is :
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A’s one day’s work = 1 6 B’s one day’s work = 1 12
(A + B)’s one day’s work= 1 + 1 = 2 + 1 = 1 6 12 12 4
table>(A + B)’s three day’s work = 3 4 Remaining work = 1 - 3 = 1 4 4
∴ Total required number of days= 1 × 12 + 3 = 3 + 3 = 6 days 4 1
Aliter : Using Rule 20,
Here, m = 6, n= 12, and p = 3
Time taken by B= mn - (m + n)p m = 6 × 12 - (6 + 12) × 3 6 = 72 - 54 = 3 days 6
∴ Total number of days taken to finish the works = 6 daysCorrect Option: C
A’s one day’s work = 1 6 B’s one day’s work = 1 12
(A + B)’s one day’s work= 1 + 1 = 2 + 1 = 1 6 12 12 4
table>(A + B)’s three day’s work = 3 4 Remaining work = 1 - 3 = 1 4 4
∴ Total required number of days= 1 × 12 + 3 = 3 + 3 = 6 days 4 1
Aliter : Using Rule 20,
Here, m = 6, n= 12, and p = 3
Time taken by B= mn - (m + n)p m = 6 × 12 - (6 + 12) × 3 6 = 72 - 54 = 3 days 6
∴ Total number of days taken to finish the works = 6 days
- A can do a piece of work in 12 days and B can do it in 18 days. They work together for 2 days and then A leaves. How long will B take to finish the remaining work ?
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(A+B)’s 2 days’ work
= 2 
1 + 1 
= 10 12 18 36
Remaining work= 1 - 10 = 26 36 36 Time taken by B to complete 26 part of work 36 = 26 × 18 = 13 days 36
Aliter : Using Rule 20,
Here, m = 12, n = 18, p = 2
Time taken by B= mn - p (m + n) m = 12 × 18 - 2(12 + 18) 12 = 216 - 60 = 13 days 12 Correct Option: D
(A+B)’s 2 days’ work
= 2 1 + 1 = 10 12 18 36
Remaining work= 1 - 10 = 26 36 36 Time taken by B to complete 26 part of work 36 = 26 × 18 = 13 days 36
Aliter : Using Rule 20,
Here, m = 12, n = 18, p = 2
Time taken by B= mn - p (m + n) m = 12 × 18 - 2(12 + 18) 12 = 216 - 60 = 13 days 12
- A and B can do a work in 18 and 24 days respectively. They worked together for 8 days and then A left. The remaining work was finished by B in :
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∵ A can finish the work in 18 days
∴ A’s one day’s' work= 1 18
Similarly, B’s one day’s work= 1 24
∴ (A + B)’s 8 days’ work= 1 + 1 × 8 18 24 = 7 × 8 = 7 72 9 ∴ Remaining work = 1 - 7 = 2 9 9
∴ Time taken to finish the remaining work by B is2 × 24 9 2 × 24 9
Aliter : Using Rule 20,
Here, m = 18, n= 24 and p = 8
⇒ Required Time= 18 × 24 - 8(18 + 24) 18 = 432 - 336 = 96 18 18 = 16 = 5 1 days 3 3 Correct Option: B
∵ A can finish the work in 18 days
∴ A’s one day’s' work= 1 18
Similarly, B’s one day’s work= 1 24
∴ (A + B)’s 8 days’ work= 1 + 1 × 8 18 24 = 7 × 8 = 7 72 9 ∴ Remaining work = 1 - 7 = 2 9 9
∴ Time taken to finish the remaining work by B is2 × 24 9 2 × 24 9
Aliter : Using Rule 20,
Here, m = 18, n= 24 and p = 8
⇒ Required Time= 18 × 24 - 8(18 + 24) 18 = 432 - 336 = 96 18 18 = 16 = 5 1 days 3 3
- A can do a piece of work in 30 days while B can do it in 40 days. In how many days can A and B working together do it ?
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A’s 1 day’s work = 1 30 B’s 1 day’s work = 1 40
∴ (A + B)’s 1 day’s work= 1 + 1 30 40 = 4 + 3 = 7 120 120 ∴ Required time = 120 = 17 1 days 7 7 Correct Option: C
A’s 1 day’s work = 1 30 B’s 1 day’s work = 1 40
∴ (A + B)’s 1 day’s work= 1 + 1 30 40 = 4 + 3 = 7 120 120 ∴ Required time = 120 = 17 1 days 7 7
- A and B can do a piece of work in 20 days and 12 days respectively. A started the work alone and then after 4 days B joined him till the completion of the work. How long did the work last ?
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A’s 1 day’s work = 1 20 A’s 4 days’ work = 4 = 1 20 5 Remaining work = 1 - 1 = 4 5 5
This part is completed by A and B together.
Now, (A + B)’s 1 day’s work= 1 + 1 20 12 = 3 + 5 = 8 = 2 60 60 15 Now, 2 work is done by (A + B) in 1 day. 15 ∴ 4 work is done in 5 = 15 × 4 = 6 days 2 5
Hence, the work lasted for 4 + 6 = 10 days.Correct Option: A
A’s 1 day’s work = 1 20 A’s 4 days’ work = 4 = 1 20 5 Remaining work = 1 - 1 = 4 5 5
This part is completed by A and B together.
Now, (A + B)’s 1 day’s work= 1 + 1 20 12 = 3 + 5 = 8 = 2 60 60 15 Now, 2 work is done by (A + B) in 1 day. 15 ∴ 4 work is done in 5 = 15 × 4 = 6 days 2 5
Hence, the work lasted for 4 + 6 = 10 days.
