# Time & Work (3)

1. P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?
1. 8
2. 5
3. 4
4. 6

Explanation :-

Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – (2/3)= 1/3
Time taken By P to do remaning work   = (1/3) / (1/18) = 6

2. 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?
1. 50
2. 40
3. 30
4. 20

Explanation :-

1 Day work of (3m +7w) = 1/10
1 Day work of (4m +6w) = 1/8
4m + 6w = 1/8   ————- Multiply by 3
3m + 7w = 1/10 ————- Multiply by 4
12m + 18w = 1/10 ————-(1)
12m +28w = 1/8 ————-(2)
By Subtracting  equation (2) from (1)
We get ,
10w = 1/40
Therefore , Work done by 10 women in 1 day =1/40
10 women can complete the work in 40 days

3. A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work?
1. 60
2. 50
3. 40
4. 30

Explanation :-

Work done by A & B in 1 day = 1/30
Work done by A & B in 20 days = 20 × (1/30) = 20/30 = 2/3
Remaining work = 1 – (2/3) = 1/3
A completes 1/3 work in 20 days
Therefore ,  A can complete the whole work in 3*20 = 60 days

4. A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in — days.
1. 5 5⁄11
2. 4 5⁄11
3. 6 4⁄11
4. 6 5⁄11

Explanation :-

A can complete the work in 12 days working 8 hours a day
Hours taken by A to complete the work = 12×8 = 96 hours
Work done by A in 1 hour = 1/96
B can complete the work in 8 days working 10 hours a day
Hours taken by B to complete the work = 8×10 = 80 hours
Work done by B in 1 hour = 1/80
Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480
Hours taken by A & B together to complete the work = 480/11 hours
A & B works 8 hours a day
Therefore ,
Total days taken by A& B together to  complete the work = (480/11)/ (8)
=> 60/11 days = 5 511 days

5. P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?
1. 9
2. 11
3. 13
4. 15