Time and Work Mcqs

A leak in the lower portion of a tank can empty the full tank in 9 hrs.  An inlet pipe fills water at the rtae of 10 lit. a minute.  When the tank is full, the inlet is opened and due to leak, the tank is empty in 16 hrs.  How many litres does the cistern hold ?

by
A leak in the lower portion of a tank can empty the full tank in 9 hrs.  An inlet pipe fills water at the rtae of 10 lit. a minute.  When the tank is full, the inlet is opened and due to leak, the tank is empty in 16 hrs.  How many litres does the cistern hold ?

A. 12,342 litres.
B. 12,444 litres
C. 12,566 litres.
D. None of thes

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

by
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
Part of work completed by A in a day = 1/X Part of work completed by B in a day
= 1/(X+5) (1/X)+(1/(X+5)) = 1/6 (2X+5)/(X²+5X) = 1/6 X²+5X = 6(2X+5) X²-7X-30=0 Solving, X=10

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

by
Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

A. 2700
B. 1080
C. 450
D. 1800
Number of bottles produced by 1 machine in a minute
= 270/6 Number of bottles produced by 10 machines in 4 minutes
= (270/6)*10*4 = 1800

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?

by
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
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 = 1/8 —(1)
q + r= 1/12 —(2)
p+ q+ r = 1/6 —(3)
(3) – (2) => p = 1/6 – 1/12 = 1/12
(3) – (1) => r = 1/6 – 1/8 = 1/24
p + r = 1/12 + 1/24 = 3/24 = 1/8
=> P and R will finish the work in 8 days

10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?

by
10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?

A. 7
B. 5
C. 6
D. 4
Work done by 10 men in 1 day = 1/7
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 10 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/140
Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)
= 5/70 + 10/140 = 1/7
=> 5 men and 10 women can complete the work in 7 days

P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in__________?

by
P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in__________?

A. 30 days
B. 25 days
C. 20 days
D. 15 days
Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/50
Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as
Work done by P in 1 day × 2 = 6/50
=> Work done by P in 1 day = 3/50
=> Work done by Q and R in 1 day = 3/50
Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25
So Q alone can do the work in 25 days

A leak in the bottom of a tank can empty the full tank in 6 hrs.  An inlet pipe fills water at the rate of 4 lit. a minute.  When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hrs.  The capacity of the tank in liters is_________?

by
A leak in the bottom of a tank can empty the full tank in 6 hrs.  An inlet pipe fills water at the rate of 4 lit. a minute.  When the tank is full, the inlet is opened and due to the leak, the tank is empty in 8 hrs.  The capacity of the tank in liters is_________?

A. 5,750 litres
B. 5,760 litres
C. 6,890 litres
D. None of these

A tap can fill a tank in 32 min. and another can empty it in 16 min.  If the tank is already half full and both the tanks are opened together, the tank will be_________?

by
A tap can fill a tank in 32 min. and another can empty it in 16 min.  If the tank is already half full and both the tanks are opened together, the tank will be_________?

A. 12 min
B. 14 min
C. 16 min
D. 20 min
In this problem, rate of water pipe (waste) is more, the tank will be emptied when the pipes are opened.
Work done in total emptying in 1 min.
=1/16−1/32=1/32
Now, full tank will be emptied by them in 32 minutes.
Half full tank will be emptied in 16 minutes.