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## Arithmetic : Level 2 Test -10

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Question 1 |

Construction of a road was entrusted to a civil engineer. He was to finish the work in 124 days for which he employed 120 workers. Two-thirds of the work was completed in 64 days. How many workers can be reduced now without affecting the completion of the work on time?

80 | |

64 | |

56 | |

24 |

Question 1 Explanation:

Let the total work is 124 x 120 = 14880 units

Work done in 64 days = 2/3 x 14880 = 9920 units

Remaining days = 60

Remaining work = 1/3 of the totalÂ = 1/3 x 14880 = 4960

We know M1 x D1 x W1 = M2 x D2 x W2

120 x 64 /9920 = M2 x 60 /4960

M2 = 64

Reduced workmen would be = 120 â€“ 64 = 56

Work done in 64 days = 2/3 x 14880 = 9920 units

Remaining days = 60

Remaining work = 1/3 of the totalÂ = 1/3 x 14880 = 4960

We know M1 x D1 x W1 = M2 x D2 x W2

120 x 64 /9920 = M2 x 60 /4960

M2 = 64

Reduced workmen would be = 120 â€“ 64 = 56

Question 2 |

Anu can complete a work in 10 days. Manu is 25% more efficient than Anu and Sonu is 60% more efficient than Manu. Working together, how long would they take to finish the job?

2 ^{6}/_{17} days | |

5 ^{6}/_{7} days | |

3 ^{5}/_{8} days | |

4 ^{5}/_{8} days |

Question 2 Explanation:

Anuâ€™s one day work = 1/10

25% of 10 = 2.5

So Manuâ€™s one day work would be = 1/12.5 = 1/8

Similarly Sonuâ€™s one day work would be = 160/100 x 1/8 = 1/5

Total work done in one day when all work together = 1/10 + 1/8 + 1/5 = 17/40

Total days = 40/17 = 2

25% of 10 = 2.5

So Manuâ€™s one day work would be = 1/12.5 = 1/8

Similarly Sonuâ€™s one day work would be = 160/100 x 1/8 = 1/5

Total work done in one day when all work together = 1/10 + 1/8 + 1/5 = 17/40

Total days = 40/17 = 2

^{6}/_{17}days therefore option a is the right answerQuestion 3 |

Working 7 h daily, 24 men can complete a piece of work in 27 days. In how many days would 14 men complete the same piece of work working 9 h daily?

29 days | |

39 days | |

36 days | |

30 days |

Question 3 Explanation:

m1 x d1 x t1 / w1 = m2 x d2 x t2 / w2

d2 = {24 x 27 x 7} / 14 x 9 = 36 days

d2 = {24 x 27 x 7} / 14 x 9 = 36 days

Question 4 |

If 15 men or 24 women or 36 boys can do a piece of work in 12 days, working 8 h a day, how many men must be associated with 12 women and 6 boys to do another piece of work 2.25 times in 30 days working 6 h in a day?

9 | |

7 | |

5 | |

8 |

Question 4 Explanation:

Ratio of men : women : boys = 15 : 24 : 36 = 5 : 8 : 12

To solve further we have to converts the women and boys in terms of men

12B = 5M

1B = 5/12M

6B = 5/12 X 6 = 5/2M

Similarly

8W = 5M

1W = 5/8M

12W = 5/8 X 12 = 15/2M

Total power in terms of men = 15/2 + 5/2 = 20/2 = 10M

Now let p be the number of men which is required

P + 10 = {15 x 12 x 8 x 2.25} / 30 x 6 = 18

Therefore the number of men required are 18 = P + 10 = 8

To solve further we have to converts the women and boys in terms of men

12B = 5M

1B = 5/12M

6B = 5/12 X 6 = 5/2M

Similarly

8W = 5M

1W = 5/8M

12W = 5/8 X 12 = 15/2M

Total power in terms of men = 15/2 + 5/2 = 20/2 = 10M

Now let p be the number of men which is required

P + 10 = {15 x 12 x 8 x 2.25} / 30 x 6 = 18

Therefore the number of men required are 18 = P + 10 = 8

Question 5 |

Two cogged wheels of which one has 16 cogs and the other 27, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 s?

26 | |

25 | |

24 | |

27 |

Question 5 Explanation:

Three quarters of a minute = Â¾ x 60 = 45 s

Therefore , 27 turns into 80 in 45 s

Therefore 16 cogs in 8 sec will turns to {27 x 80 x 8}/ 16 x 45

=24 times

Therefore , 27 turns into 80 in 45 s

Therefore 16 cogs in 8 sec will turns to {27 x 80 x 8}/ 16 x 45

=24 times

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