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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?

24 days | |

10 days | |

32 days | |

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

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?

8 am | |

7 am | |

5 am | |

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

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.

3 min | |

6 min | |

5 min | |

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)

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 4

^{1}/_{2}h. It now takes 1/2 h longer. If the cistern is full, in how much time would the leakage empty the full cistern?23 h | |

35 h | |

52 h | |

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

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?

16 days | |

15 days | |

17 days | |

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

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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