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Arithmetic: Time and Work Test-3

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Question 1
9 children can complete a piece of work in 360 days. 18 men can complete the same piece of work in 72 days and 12 women can complete the piece of work in 162 days. In how many days can 4 men, 12 women and 10 children together complete the piece of work?
A
124
B
81
C
68
D
96
Question 1 Explanation: 
Let the work be of 720x9 units.
Every day the each child does$ \displaystyle \frac{720\times 9}{9\times 360}=2\,unit\,\,of\,work$
Every day the man can do $ \frac{720\times 9}{72\times 18}=5\,unit\,\,of\,\,work$
Every day 1 woman does  =$ \displaystyle \frac{720\times 9}{162\times 12}=\frac{10}{3}\,units\,\,of\,\,work$
4 men can do 4x5= 20 units of work per day.
12 women can do 12x10/3= 40 units of work per day.
10 children can do 10x2= 20 units of work per day
Total units per day= 20+40+20 = 80 units of work.
Therefore number of days required is 720x9/80 = 81 days.
Question 2
Fifty six men can complete a piece of work in 24 days. In how many days can 42 men complete the same piece of work?
A
18
B
32
C
98
D
48
Question 2 Explanation: 
The number of days if inversely proportional to the men working.
Lesser the men, more the number of days.
Required number of days = $ \frac{56\times 24}{42}=32$
The correct option is 32 days
Question 3
6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day how many men would be required totally?
A
36
B
24
C
18
D
Cannot be determined
Question 3 Explanation: 
Let the total work be 360 units.
6 men can do 360 units in 12 days.
Therefore, 1 man can do 360/(6x12)=5 units in 1 day.
Thus 4 men can do 4x5 = 20 units in 1 day.
8 women do 360 units in 18 days.
1 woman does= 360/(8X18) = 5/2 units per day.
12 women does 12x5/2 = 30 units per day.
18 children do 360 units of work in 10 days.
1 child does 360/(18x10) = 2 units per day.
20 children do 20x2 = 40 units of work per day.
Total = 20+30 + 40 = 90 units of work per day.
In 2 days 90 x 2 = 180 units completed.
Remaining = 360- 180 = 180 units of work left.
1 man can do 5 units of work in 1 day.
To finish 180 units in one day 180/5 = 36 men is required.
Question 4
2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?
A
4
B
8
C
6
D
Cannot be determined
Question 4 Explanation: 
Let the total work be 360 units of work .
2 men complete 360 units in 6 days.
1 man completes 360/(2X6) = 30 units in 1 day.
2 women can complete 360 units of work in 9 days.
1 woman can complete 360/(2X9)= 20 units in 1 day.
3 women can complete 20X3 = 60 units of work in 1 day.
3 children can finish 360 units in 8 days.
1 child can do 360 / (3X8) = 15 units in 1 day.
4 children can finish do 15X4= 60 units of work in 1 day.
Total = 60+60 = 120 units of work.
Left = 360-120 = 240 units of work .
Total men required to finish the work in 1 day is 240/30 = 8 men.
Question 5
4 men can complete a piece of work in 2 days. 4 women can complete the same piece of work in 4 days whereas 5 children can complete the same piece of work in 4 days. If, 2 men, 4 women and 10 children work together, in how many days can the work be completed?
A
1 day
B
3 days
C
2 days
D
4 days
Question 5 Explanation: 
Since 4 men can do a work in 2 days we can say that 2 men can do in 4 days.
4 women can do in 4 days
5 children can also do the same work in 4 days
2 men ≡ 4 women ≡ 5 children
Therefore, 2 men + 4 women + 10 children = 2 +2 +4 men = 8 men.
Since 4 men do the work in 2 days.
We can conclude that 8 men can do the work in 1 day.
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