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## Arithmetic: Time and Work Test-4

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Question 1 |

Ayesha can complete a piece of work in 16 days. Amita can complete the same piece of work in 8 days. If both of them work together in how many days can they complete the same piece of work?

6 days | |

$ \displaystyle 4\frac{2}{5}$ days | |

$ \displaystyle 5\frac{1}{3}$ days | |

12 days |

Question 1 Explanation:

Let the work be 16 units.

Ayesha does 1 unit/day.

Amita does 2 units / day.

Ayesh+ Amita does (1+2) = 3 units/ day.

Total number of days required is 16/3 = 5 1/3 days.

Ayesha does 1 unit/day.

Amita does 2 units / day.

Ayesh+ Amita does (1+2) = 3 units/ day.

Total number of days required is 16/3 = 5 1/3 days.

Question 2 |

Two cyclists start on a circular track from a given point but in opposite directions with speeds of 7 m/s and 8 m/s respectively. If the circumference of the circle is 300 m, after what time will they meet at the starting point?

20 s | |

100 s | |

300 s | |

200 s |

Question 2 Explanation:

The relative speed is 8-7 =1 m/s.

Therefore, 300 m can be traveled in 300 secs.

Thus in 300 secs, the cyclist will meet for the first time.

Therefore, 300 m can be traveled in 300 secs.

Thus in 300 secs, the cyclist will meet for the first time.

Question 3 |

42 women can do a piece of work in 18 days. How many women would be required do the same work in 21 days?

36
| |

24 | |

30 | |

44 |

Question 3 Explanation:

In 18 days the number of women required to finish the work is 42.

In 1 day the number of women required to finish the work is 42 x 18.

Therefore, in 21 days the number of women required to finish the work is 42 x 18/21= 36 days.

In 1 day the number of women required to finish the work is 42 x 18.

Therefore, in 21 days the number of women required to finish the work is 42 x 18/21= 36 days.

Question 4 |

A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is:

11 | |

21 | |

28 | |

42 |

Question 4 Explanation:

Let A do 2p units work in 1 day and thus B does p units in 1 day.

Together they finish the work in 14 days @(1+2)=3p units of work per day.

Total work = 14 x 3p = 42p units of work.

A does 42x units of work in 42p/2p= 21 days.

Together they finish the work in 14 days @(1+2)=3p units of work per day.

Total work = 14 x 3p = 42p units of work.

A does 42x units of work in 42p/2p= 21 days.

Question 5 |

A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. Making four more pieces per day that was planned, they could complete the job a day ahead of schedule. How many days did they take to complete the job?

8 days | |

10 days | |

9 days | |

12 days |

Question 5 Explanation:

Let us do this by options.

We must understand that whatever be the answer (say X) it must be a factor of 360 .

Therefore X and X-1 must be factors of 360.

Let us see the factors of 360 = 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20â€¦..

We can see that 9 and 10 are factors of 360.

And we knew that X and X-1 are the days.

Therefore X=10.

We must understand that whatever be the answer (say X) it must be a factor of 360 .

Therefore X and X-1 must be factors of 360.

Let us see the factors of 360 = 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20â€¦..

We can see that 9 and 10 are factors of 360.

And we knew that X and X-1 are the days.

Therefore X=10.

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