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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?
12 min
24 min
30 min
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.
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.
25 km/h
40 km/h
35 km/h
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?
15 days
18 days
24 days
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?
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?
10: 27
1: 3
1: 2
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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