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## Arithmetic: Time and Work Test-8

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*Arithmetic: Time and Work Test-8*. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

Manoj and Ajita can do a job alone in 10 days and 12 days respectively. Manoj starts the work and after 6 days Ajita also joins to finish the work together. For how many days did Ajita actually worked on the job?

2 ^{3}/_{11} | |

2 ^{1}/_{11} | |

2 ^{2}/_{11} | |

3 ^{1}/_{12} |

Question 1 Explanation:

For the 6 days work done by Manoj= 6/10 = 3/5

Therefore the remaining work = 1 – 3/5 = 2/5

Now they both can complete the remaining work in 2/5{(10 x 12)/(10+12)}

Now question asks about work done by Ajita so Ajita did work for

2

Therefore the remaining work = 1 – 3/5 = 2/5

Now they both can complete the remaining work in 2/5{(10 x 12)/(10+12)}

Now question asks about work done by Ajita so Ajita did work for

2

^{2}/_{11}daysQuestion 2 |

Ashokan is thrice as good a workman as Nitin and is therefore able to finish a piece of work in 40 days less than Nitin. Find the time in which they can do it working together.

15 days | |

7 days | |

16 days | |

13 days |

Question 2 Explanation:

Let us assume that the work done by Ashokan = w days

So the time taken by Nitin = 3w

So according to the question

3w – w = 40

W = 20 day

And 3w = 60 days

So therefore together they can finish the work in {(20 x 60)/(20 + 60)} = 15days

So the time taken by Nitin = 3w

So according to the question

3w – w = 40

W = 20 day

And 3w = 60 days

So therefore together they can finish the work in {(20 x 60)/(20 + 60)} = 15days

Question 3 |

A alone would take 8 more days to complete the job than if both A and B worked together. If B worked alone, he took four and half more days to complete the job than if A and B worked together. How many days would they take if both A and B worked together?

8 days | |

5 days | |

2 days | |

6 days |

Question 3 Explanation:

Let us assume both can complete the work in w days

And we are given the statements that A can complete the work in 8 more days in comparison to when they worked together.

So, we can say that A can complete the work in (w+8) days

In one day, A completes 1/ (w+8) units of work.

Similarly, in one day, B completes 1/(w+4.5) units of work.

Combined work by A and B in one day = {1/ (w+8)} + {1/(w+4.5)}

Now this should be equal to 1/w units of work.

Equating the two,

{1/ (w+8)} + {1/(w+4.5)} = 1/w

We can see that 6 satisfies the above equation.

Thus, option (d) is the correct answer.

And we are given the statements that A can complete the work in 8 more days in comparison to when they worked together.

So, we can say that A can complete the work in (w+8) days

In one day, A completes 1/ (w+8) units of work.

Similarly, in one day, B completes 1/(w+4.5) units of work.

Combined work by A and B in one day = {1/ (w+8)} + {1/(w+4.5)}

Now this should be equal to 1/w units of work.

Equating the two,

{1/ (w+8)} + {1/(w+4.5)} = 1/w

We can see that 6 satisfies the above equation.

Thus, option (d) is the correct answer.

Question 4 |

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 4 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 that this 7/8 work 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 together both would 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 that this 7/8 work 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 together both would completes the work in 15 days .

Question 5 |

Madhu takes twice as much time as Uma to complete a work and Ramesh does it in the same time as Madhu and Uma together would. If all three are working together, they can finish the work in 6 days. Then the time taken by Madhu to finish the work is ___?

12 days | |

14 days | |

36 days | |

40 days |

Question 5 Explanation:

We will assume that Madhu can complete the work in 2D days

So Uma can complete the work in D days

So both they can complete the work in {2D x D/2D+D} = 2/3D

Now according to the question we can say that

1/2D + 1/D +3/2D = 1/6

6/2D = 1/6

2D = 36

So Madhu can do the work in 36 days

So Uma can complete the work in D days

So both they can complete the work in {2D x D/2D+D} = 2/3D

Now according to the question we can say that

1/2D + 1/D +3/2D = 1/6

6/2D = 1/6

2D = 36

So Madhu can do the work in 36 days

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