Time and Work
- A certain number of men can do a work in 60 days. If there were eight more men, it could be completed in 10 days less. How many men were there in the beginning?
-
View Hint View Answer Discuss in Forum
Let the number of men in the beginning = x
Then, x + 8 = 60 x 50 ⇒ x + 8 = 6 x 5
⇒ 6x = 5x + 40 Þ x = 40
Aliter : Using Rule 23,
Here, D = 60, a = 8, d = 10
Required number= a(D - d) d = 8(60 - 10) = 40 10 Correct Option: D
Let the number of men in the beginning = x
Then, x + 8 = 60 x 50 ⇒ x + 8 = 6 x 5
⇒ 6x = 5x + 40 Þ x = 40
Aliter : Using Rule 23,
Here, D = 60, a = 8, d = 10
Required number= a(D - d) d = 8(60 - 10) = 40 10
- 12 persons can do a piece of work in 4 days. How many persons are required to complete 8 times the work in half the time ?
-
View Hint View Answer Discuss in Forum
12 persons can complete a
work in 4 days.
⇒ 24 persons can complete the
work in 2 days.
⇒ 24 persons can complete the
8 times work in 16 days
⇒ 24 × 8 persons = 192 persons can complete the 8 times
work in 2 days.
Aliter : Using Rule 1,
Here, M1 = 12, W1 = 1, D1 = 4
M2 = ?, W2 = 8, D2 = 2
M1D1W2 = M2D2W1
12 × 4 × 8 = M2 × 2 × 1
M2 = 192Correct Option: A
12 persons can complete a
work in 4 days.
⇒ 24 persons can complete the
work in 2 days.
⇒ 24 persons can complete the
8 times work in 16 days
⇒ 24 × 8 persons = 192 persons can complete the 8 times
work in 2 days.
Aliter : Using Rule 1,
Here, M1 = 12, W1 = 1, D1 = 4
M2 = ?, W2 = 8, D2 = 2
M1D1W2 = M2D2W1
12 × 4 × 8 = M2 × 2 × 1
M2 = 192
- A work could be completed in 100 days by some workers. However, due to the absence of 10 workers, it was completed in 110 days. The original number of workers was :
-
View Hint View Answer Discuss in Forum
Let the original number of
workers = x. Then,
x × 100 = (x – 10) × 110
⇒ 10x = 11x – 110
⇒ x = 110
Aliter : Using Rule 23,
Here, D = 100, a = 10,
d = (110 - 100) = 10
Required number= a(D + d) d = 10(100 + 10) = 110 10 Correct Option: B
Let the original number of
workers = x. Then,
x × 100 = (x – 10) × 110
⇒ 10x = 11x – 110
⇒ x = 110
Aliter : Using Rule 23,
Here, D = 100, a = 10,
d = (110 - 100) = 10
Required number= a(D + d) d = 10(100 + 10) = 110 10
- A job can be completed by 12 men in 12 days. How many extra days will be needed to complete the job if 6 men leave after working for 6 days ?
-
View Hint View Answer Discuss in Forum
Work done by 12 men in 6 days
= 1 2
Remaining work= 1 - 1 = 1 2 2
6 men leave the work.∴ Time taken = 12 × 12 = 12 days 6 × 2 Correct Option: C
Work done by 12 men in 6 days
= 1 2
Remaining work= 1 - 1 = 1 2 2
6 men leave the work.∴ Time taken = 12 × 12 = 12 days 6 × 2
- 60 men could complete a work in 250 days. They worked together for 200 days. After that the work had to be stopped for 10 days due to bad weather.
How many more men should be engaged to complete the work in time ?
-
View Hint View Answer Discuss in Forum
Using Rule 1,
60 men can complete a work in 250 days.
∴ Work done by 60 men in 1 day= 1 250
⇒ Work done by 60 men in 200 days= 200 = 4 250 5
Remaining work= 1 - 4 = 1 5 5
Work is stopped for 10 days.
Now, 1/5 work is to be complete by x men in 40 days.
60 men can complete 1/5 work in 50 days.
∴ 40 : 50 : : 60 : x
⇒ 40 x = 50 × 60⇒ x = 50 × 60 = 75 40
Hence, 15 more men should be engagedCorrect Option: B
Using Rule 1,
60 men can complete a work in 250 days.
∴ Work done by 60 men in 1 day= 1 250
⇒ Work done by 60 men in 200 days= 200 = 4 250 5
Remaining work= 1 - 4 = 1 5 5
Work is stopped for 10 days.
Now, 1/5 work is to be complete by x men in 40 days.
60 men can complete 1/5 work in 50 days.
∴ 40 : 50 : : 60 : x
⇒ 40 x = 50 × 60⇒ x = 50 × 60 = 75 40
Hence, 15 more men should be engaged
