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## Arithmetic : Level 2 Test -8

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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 workmen. Two-thirds of the work was completed in 64 days. How many workmen can be reduced now without affecting the completion of the work on time?

80 | |

64 | |

56 | |

24 |

Question 1 Explanation:

Let us assume the total work is done by the worker = 124 x 120 = 14880 units

Two-thirds of the work was completed in 64 days

Therefore work done by the workers in 64 days = 2/3 x 14880 = 9920

Work left = 14880-9920 = 4960

Number of days left = 124-64 = 60

Now we have a relation for this

(M1 x D1) / W1 = (M2 x D2) / W2

(120 x 64)/9920 = (M2 x 60)/4960

M2 = 64

Therefore number of workers left will be 120 -64 = 56 men

Two-thirds of the work was completed in 64 days

Therefore work done by the workers in 64 days = 2/3 x 14880 = 9920

Work left = 14880-9920 = 4960

Number of days left = 124-64 = 60

Now we have a relation for this

(M1 x D1) / W1 = (M2 x D2) / W2

(120 x 64)/9920 = (M2 x 60)/4960

M2 = 64

Therefore number of workers left will be 120 -64 = 56 men

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} | |

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

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

4 ^{5}/_{8 } |

Question 2 Explanation:

Anu can do work in one day = 1/10

Work done by Manu in one day = 125/100 x 1/10 = 1/8

Work done by Sonu in one day = 160 /100 x 1/8 = 1/5

Total work done by all of themÂ = 1/10 + 1/8 + 1/5 = 17/40

Number of days = 40/17 = 2

Work done by Manu in one day = 125/100 x 1/10 = 1/8

Work done by Sonu in one day = 160 /100 x 1/8 = 1/5

Total work done by all of themÂ = 1/10 + 1/8 + 1/5 = 17/40

Number of days = 40/17 = 2

^{6}/_{17 }daysQuestion 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:

Now we have a relation for this

(M1 x D1 x T1 ) / W1 = (M2 x D2 x T 2) / W2

As work is same hence W1 = W2

Number of days are required = (24 x 27 x 7) / 14 x 9 = 36 days

(M1 x D1 x T1 ) / W1 = (M2 x D2 x T 2) / W2

As work is same hence W1 = W2

Number of days are required = (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 Â work in 12 days, working 8 h a day, how many men Â must be associated with 12 women and 6 boys to do Â another piece of work 2.25 times in 30 days working Â 6 h in a day?

9 | |

7 | |

5 | |

8 |

Question 4 Explanation:

Ratio of M : W : B = 15 : 24 : 36 = 5 : 8 : 12

Now we have to convert it in terms of manâ€™s work 8W = 5M

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

12B = 5M

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

Now work in terms of men = 15/2 + 5/2 = 20/2 =10M

If we have T men then

T + 10 = (15 x 12 x 8 x 2.25)/ 30 x 6 = 18

T + 10 = 18

T= 8

Now we have to convert it in terms of manâ€™s work 8W = 5M

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

12B = 5M

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

Now work in terms of men = 15/2 + 5/2 = 20/2 =10M

If we have T men then

T + 10 = (15 x 12 x 8 x 2.25)/ 30 x 6 = 18

T + 10 = 18

T= 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:

Â¾ x 60 = 45s

27 cogs turn 80 times in 45 sec.

16 cogs in 8s = (27 x 80 x 8 )/ 16 x 45 = 24 times

27 cogs turn 80 times in 45 sec.

16 cogs in 8s = (27 x 80 x 8 )/ 16 x 45 = 24 times

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