851. A can do (1/3) of a work in 5 days and B can do (2/5) of the work in 10 days. In how many days both A and B together can do the work ?
A. 75/8 days
B. 44/6 days
C. 48/5 days
D. None of these

852. 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

Explanation:
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

853. 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

Explanation:
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

854. 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

Explanation:
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

855. 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

Explanation:
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

856. 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

Explanation:
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

857. 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

858. 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

Explanation:
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.

859. A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. A alone can do the work in__________?
A. 20 days
B. 30 days
C. 40 days
D. none of these

860. Twelve men can do a work in twenty days while twenty women can finish the same work in sixteen days. Find the ratio between the capacity of a man and a woman.
A. 3:4
B. 5:4
C. 4:3
D. 5:3

Explanation:
Part of work completed by a man in a day = 1/(12*20)
= 1/240 Part of work completed by a woman in a day = 1/(20*16) = 1/320 Ratio of their capacities
= (1/240):(1/320) = 320:240 = 4:3