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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?
A
80
B
64
C
56
D
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
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?
A
2 6/17
B
5 6/7
C
3 5/8
D
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 them  = 1/10 + 1/8 + 1/5 = 17/40
Number of days = 40/17 = 26/17 days
Question 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?
A
29 days
B
39 days
C
36 days
D
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
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?
A
9
B
7
C
5
D
8
Question 4 Explanation: 
Ratio of M : W : B = 15 : 24 : 36 = 5 : 8 : 12
Now we have to convert it in terms of man’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?
A
26
B
25
C
24
D
27
Question 5 Explanation: 
¾ 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
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