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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 total = 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 – 64 = 56
Work done in 64 days = 2/3 x 14880 = 9920 units
Remaining days = 60
Remaining work = 1/3 of the total = 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 – 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 | |
45/8 days |
Question 2 Explanation:
Anu’s one day work = 1/10
25% of 10 = 2.5
So Manu’s one day work would be = 1/12.5 = 1/8
Similarly Sonu’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 answer
25% of 10 = 2.5
So Manu’s one day work would be = 1/12.5 = 1/8
Similarly Sonu’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 answer
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?
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 = ¾ 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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