 # Time & Work (5)

1. P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?
1. 4
2. 5
3. 6
4. 7

Explanation :-

Let P completes the work in x days
Therefore,  Q completes the work in x/2 days  &  R completes the work in x/3 days
P’s 1 day work  = 1/x
Q’s 1 day work = 1/(x/2) = 2/x
R’s 1 day work = 1/(x/3) = 3/x
(P+Q+R)’s 1 day work = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x
6/x = 2 , x = 12
Time taken by Q to complete the work = 12/2 = 6 days

2. P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in — days.
1. 12
2. 16
3. 20
4. 24

Explanation :-

P’s 1 day  Work = 1/15
Q’s 1 day  Work = 1/10
Work done by P & Q together in 1 day = 1/15 + 1/10 = 1/6
Work done by P & Q in 2 days = 2 × (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
P completes the remaining work in = (2/3) / (1/15) = 10 days
Total time = 2 + 10 = 12 days

3. P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?
1. 10
2. 15
3. 18
4. 22

Explanation :-

(P + Q)’s 1 day work = 1/30 ———-(1)
(Q + R)’s 1 day work = 1/24 ———-(2)
(P + R)’s 1 day work = 1/20 ———-(3)
By additing equation (1) ,(2) & (3)
2(P+Q+R)’s 1 day work = (1/30) + (1/24) + (1/20) =  1/8
(P+Q+R)’s 1 day work = (1/8)/2 = 1/16
(P+Q+R)’s 10 day work = 10/16 = 5/8
Remaining work = 1 – (5/8) = 3/8
P’s 1 day work = (1/16)- (1/24) = 1/48 P completes the remaining work in  = (3/8) / (1/48) = 18 days
P completes the remaining work in  = (3/8) / (1/48) = 18 days

4. P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in — days
1. 1
2. 2
3. 3
4. 4

Explanation :-

Q completes the work in 12 days , Therefore P competes it in 6 days
P’s 1 day work = 1/6    &       Q’s 1 day work = 1/12
1 day work of P & Q together = (1/6) + (1/12) = 3/12 = 1/4
Therefore , P & Q together completes the work in 4 days

5. A work can be finished in 16 days by 20 women. The same work can be finished in 15 days by 16 men. The ratio between the capacity of a man and a woman is
1. 1:3
2. 4:3
3. 2:3
4. 2:1