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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.

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 fillsÂ 6 units /min and B fills Â 2 units/min.

Total = 8 units/min.

A+B can fill the tank in 96/8 = 12 min.

Correct option is (a)

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 fillsÂ 6 units /min and B fills Â 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}$

$ 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.

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?

Boys | |

Girls | |

Women | |

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

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 â€“ 2.5 - .5 = 3 hrs.

Therefore the ratio of the speed of motorcycle:car = 3:6 = 1:2.

Time taken by the car is = 6 â€“ 2.5 - .5 = 3 hrs.

Therefore the ratio of the speed of motorcycle:car = 3:6 = 1:2.

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