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?

A. 10
B. 8
C. 18
D. 19

Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8
Remaining work = 1 = 5/8 = 3/8
Work done by P in 1 day = Work done by P,Q and R in 1 day – Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18

Related Mcqs:

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?
A. 8
B. 6
C. 4
D. 2
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?
A. 70
B. 50
C. 40
D. 60
A alone can finish a work in X days. B alone can finish the same work in X+5 days. Together, they take 6 days to complete the work. Find X
A. 12
B. 8
C. 10
D. 9
A and B can finish a piece of work in 20 days .B and C in 30 days and C and A in 40 days. In how many days will A alone finish the job?
A. 48
B. 34(2/7)
C. 44
D. 45
8 children and 12 men complete a certain piece of work in 9 days. If each child takes twice the time taken by a man to finish the work, in how many days will 12 men finish the same work ?
A. 6 days
B. 8 days
C. 10 days
D. 12 days
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?
A. 7
B. 8
C. 9
D. 6
Let P takes x days to complete the work
Then Q takes x/2 days and R takes x/3 days to finish the work
Amount of work P does in 1 day = 1/x
Amount of work Q does in 1 day = 2/x
Amount of work R does in 1 day = 3/x
Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x
6/x = 2
=> x = 12
=> Q takes 12/2 days = 6 days to complete the work
P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?
A. 7
B. 8
C. 9
D. 10
A alone can finish a work in 10 days and B alone can do it in 15 days. If they work together and finish, then out of a total wages of Rs.75. A will get:___________?
A. 35 Rs.
B. 40 Rs.
C. 45 Rs.
D. None of these
A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in___________days if they work together.
A. 18 days
B. 22 ½ days
C. 24 days
D. 26 days
P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?
A. 5 days
B. 10 days
C. 15 days
D. 12 days