Time and Work Mcqs

A. 120, 40, 60 days
B. 120, 60, 80 days
C. 40, 30, 120 days
D. 30, 40, 60 days
Let a: be the time in which X & Y completes their work = 30 days
b: time in which Y & Z completes their work = 24 days
c: time in which X & Z completes their work = 40 days
X alone can complete the work in (2 * a * c) / (ab + bc – ac) days
= 2 * 30 * 24 * 40 / ((30 * 24) + (24 * 40) – (30 * 40)) = 120 days
Y alone can complete the work in 2 * a * b * c / (- ab + bc + ac) days
= 2 * 30 * 24 * 40 / (-(30 * 24) + (24 * 40) + (30 * 40)) = 40 days
Z alone can complete the work in 2 * a * b * c / (ab – bc + ac) days
= 2 * 30 * 24 * 40 / ((30 * 24) – (24 * 40) + (30 * 40))
= 60 days

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

A. 5 5⁄11
B. 4 5⁄11
C. 6 4⁄11
D. 6 5⁄11
A can complete the work in 12 days working 8 hours a day
=> Number of hours A can 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
=> Number of hours B can 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
=> A and B can complete the work in 480/11 hours
A and B works 8 hours a day
Hence total days to complete the work with A and B working together
= (480/11)/ (8) = 60/11 days = 5 5⁄11 days

A. Rs. 380
B. Rs. 600
C. Rs. 420
D. Rs. 400
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 – 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3200 × (1/8) = 400

A. 5 hrs
B. 10 hrs
C. 15 hrs
D. 20 hrs

A. 7.5 hrs
B. 5 hrs
C. 7 hrs
D. None of these

A. 42/4 days
B. 41/4 days
C. 55 days
D. None of these

A. 15 days
B. 10 days
C. 8 days
D. 20 days
(4/m)+(2/w) = 1/2 2/m = 1/5 1/m = 1/10 (4/10)+(2/w) = (1/2) 2/w = 1/10 2 women alone take 10 days.

A. 32 hours
B. 48 hours
C. 3 days
D. 4 days
Part of task completed by A in a day = 1/x Part of task completed by B in a day = 3/x (B is thrice as efficient as A) (1/x)+(3/x) = 1 4/x = 1 x = 4 B completes 3/4th of the task in a day. He takes 4/3 days to complete the entire task. 4/3 days = (4/3*24) hours = 32 hours

A. 4(2/3) days
B. 4 days
C. 5(1/3) days
D. 1(1/3) days
(1/A)+(1/B) = (1/6) (1/B)+(1/C) = (1/12) (1/A)+(1/C) = (1/8) Solving the three equations,
(1/A)+(1/B)+(1/C) = (3/16) Together they take 16/3 = 5(1/3) days to complete the task.