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Arithmetic: Time and Work Test-1

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Question 1
A and B together can do a piece of work in 30 days. A and B worked for 16 days and B finished the remaining work alone in 44 days. In how many days will B finish the whole work alone?
A
24 days
B
10 days
C
32 days
D
60 days
Question 1 Explanation: 
Let A complete the work alone in P days.
Now Let us suppose A and B can do 1 unit work in 30 days
Therefore (A+B)s one day work = 1/30
Therefore Work done by B in one day alone = (1/30 -1/p)
Now If A can complete the whole work in P days
Then in 1 day A can complete 1/p of work
therefore in 16 days A can complete = 16/p
therefore remaining work would be = (1- 16/p)
Now We know that B completed the remaining work in 44 days
Therefore B's 44 days of work = 44(1/30 - 1/p)
Therefore we can say that
1-16/p = 44(1/30-1/p)
On calculating
p= 60 days
Therefore One day work of B alone = 1/30 - 1/60 = 1/60
Hence B can complete this work in 60 days
Question 2
Two pipes can fill a tank in 8 hours and 12 hours respectively whereas an escape pipe can empty it in 6 hours. If the three pipes are opened at 1 pm, 2 pm and 3 pm respectively, at what time will the tank be filled?
A
8 am
B
7 am
C
5 am
D
7.30 am
Question 2 Explanation: 
Pipe A fills 1/8 of the tank in one hour.
Pipe B fills 1/12 of the in one hour.
By 3 pm, the two pipes combine to fill 2/8 +1/12 = 1/3 part of the tank
The balance amount to be filled = 1 -1/3 = 2/3
Now we know that the escape pipe empties the tank at the rate of 1/6 portion of the tank per hour.
Let P be the total number of hours to fill 2/3 of the tank. Therefore, we know now:
(1/8 + 1/12 -1/6)p  =  2/3
By solving this p= 16
So the total time to fill the tank taken by the taps would be = 16 hours
So the time will be 3 pm + 16 hours = 7 am
Question 3
Two pipes P and Q can fill a Cistern in 3 and 6 min respectively, while an empty pipe R can empty the Cistern in 4 min. All the three pipes are opened together and after 2 min pipe R is closed. Find the time.In which tank will be full.
A
3 min
B
6 min
C
5 min
D
8 min
Question 3 Explanation: 
In two minutes the part of tank will be filled = (2/3+2/6-2/4)=1/2
Now according to the question after 2 minutes the pipe R is closed so
The half part will be now filled by the two running pipes
So In one minute they can fill = 1/3 + 1/6 = ½ part
So they will take 1 minute to fill the remained part
S the right option for this question is option (a)
Question 4
There is a leak in the bottom of a cistern. Before the leak, it could be filled in 41/2h. It now takes 1/2 h longer. If the cistern is full, in how much time would the leakage empty the full cistern?
A
23 h
B
35 h
C
52 h
D
45 h
Question 4 Explanation: 
Let the leakage will empty the tank in E h
So
(9/2 x E )/ (E – 9/2) = 5
9/2 E = 5E – 45/2
1/2E = 45/2 =45 h
Question 5
A can do a piece of work in 40 days. He starts working, but having some other engagements he drops out after 5 days. Thereafter, B completes this work in 21 days. How many days would A and B take to complete this work working together?
A
16 days
B
15 days
C
17 days
D
11 days
Question 5 Explanation: 
Work done by A in one day = 1/40
Work done by A in five days = 5/40
Therefore the remaining work = 1 – 5/40 = 7/8
So from question we are given by that this work 7/8 is done by B in 21 days
Work done by B in one day = 7/8 x 21 = 1/24
Work done by both in one day will be = 1/40 + 1/24 = 1/15
Hence both completes the work in 15 days
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