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Arithmetic: Time and Work Test-2

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Question 1
One fill pipe A is 3 times faster than second fill pipe B and takes 32 min less than the fill pipe B. When will the cistern be full if both pipes are opened together?
A
12 min
B
24 min
C
30 min
D
Data inadequate
Question 1 Explanation: 
Let the pipe B fill the tank in 3x min.
Therefore the pipe A will be filled in x min.
3x-x=32
x= 16 min.
A take 16 min to fill and B takes 48 min to fill the tank.
Let tank be of volume 96 units.
A fills  6 units /min and B fills  2 units/min.
Total = 8 units/min.
A+B can fill the tank in 96/8 = 12 min.
Correct option is (a)
Question 2
A man sitting in a train travelling at the rate of 50 km/h observes that it takes 9 s for a goods train travelling in the opposite direction to pass him. If the goods train is 187.5 m long, find its speed.
A
25 km/h
B
40 km/h
C
35 km/h
D
36 km/h
Question 2 Explanation: 
Speed of the train = 50 km/h
$ 50\times \frac{5}{18}m/s$
The goods train travels 187.5 = 375/2 m in 9 secs.
Relative speed
=$ \frac{375}{2\times 9}=\frac{375}{18}m/s$
Therefore speed of the goods train
=$ \begin{array}{l}\frac{375}{18}-\frac{250}{18}=\frac{125}{18}m/s\\=\frac{\frac{125}{18}\times 18}{5}=25km/h\end{array}$
Question 3
'A' can complete a piece of work in 12 days. 'A' and 'B' together can complete the same piece of work in 8 days. In how many days can 'B' alone complete the same piece of work?
A
15 days
B
18 days
C
24 days
D
28 days
Question 3 Explanation: 
Let the total work be of 120 units.
A does 120/12= 10 units of work per day.
A+B does 120/8 = 15 units of work per day.
B does 15-10 = 5 units of work per day.
B can finish in 120/5 = 24 days.
Question 4
4 girls can do a piece of work in 8 days, 3 boys can do the same piece of work in 9 days, 7 men do the same piece of work in 2 days and 5 women can do the same piece of work in 4 days, Who is least efficient?
A
Boys
B
Girls
C
Women
D
Men
Question 4 Explanation: 
4 girls can do a piece of work in 8 days
Therefore, 1 girl can do a piece of work in 8x4 = 32 days.
3 boys do the piece of work in 9 days.
1 boy can do the same piece of work in 9x3= 27 days
7 men do the work in 2 days.
1 man can do the work in 14 days.
5 women can do the work in 4 days.
1 women can do the work in 5x4 = 20 days.
Efficiency : Man> Woman > Boy > Girl
Question 5
A motor cyclist goes from Mumbai to Pune, a distance of 192 km, at an average speed of 32 km/h. Another man starts from Mumbai by car, $ \displaystyle 2\frac{1}{2}$ after the first and reaches Pune half an hour earlier. What is the ratio of the speeds of the motor cycle and the car?
A
10: 27
B
1: 3
C
1: 2
D
5: 4
Question 5 Explanation: 
Time required to reach by motor cycle 192/32 = 6 hrs.
Time taken by the car is = 6 – 2.5 - .5 = 3 hrs.
Therefore the ratio of the speed of motorcycle:car = 3:6 = 1:2.
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