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Arithmetic: Time and Work Test-4

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Question 1
Ayesha can complete a piece of work in 16 days. Amita can complete the same piece of work in 8 days. If both of them work together in how many days can they complete the same piece of work?
A
6 days
B
$ \displaystyle 4\frac{2}{5}$ days
C
$ \displaystyle 5\frac{1}{3}$ days
D
12 days
Question 1 Explanation: 
Let the work be 16 units.
Ayesha does 1 unit/day.
Amita does 2 units / day.
Ayesh+ Amita does (1+2) = 3 units/ day.
Total number of days required is 16/3 = 5 1/3 days.
Question 2
Two cyclists start on a circular track from a given point but in opposite directions with speeds of 7 m/s and 8 m/s respectively. If the circumference of the circle is 300 m, after what time will they meet at the starting point?
A
20 s
B
100 s
C
300 s
D
200 s
Question 2 Explanation: 
The relative speed is 8-7 =1 m/s.
Therefore, 300 m can be traveled in 300 secs.
Thus in 300 secs, the cyclist will meet for the first time.
Question 3
42 women can do a piece of work in 18 days. How many women would be required do the same work in 21 days?
A
36
B
24
C
30
D
44
Question 3 Explanation: 
In 18 days the number of women required to finish the work is 42.
In 1 day the number of women required to finish the work is 42 x 18.
Therefore, in 21 days the number of women required to finish the work is 42 x 18/21= 36 days.
Question 4
A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is:
A
11
B
21
C
28
D
42
Question 4 Explanation: 
Let A do 2p units work in 1 day and thus B does p units in 1 day.
Together they finish the work in 14 days @(1+2)=3p units of work per day.
Total work = 14 x 3p = 42p units of work.
A does 42x units of work in 42p/2p= 21 days.
Question 5
A team of workers was employed by a contractor who undertook to finish 360 pieces of an article in a certain number of days. Making four more pieces per day that was planned, they could complete the job a day ahead of schedule. How many days did they take to complete the job?
A
8 days
B
10 days
C
9 days
D
12 days
Question 5 Explanation: 
Let us do this by options.
We must understand that whatever be the answer (say X) it must be a factor of 360 .
Therefore X and X-1 must be factors of 360.
Let us see the factors of 360 = 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20…..
We can see that 9 and 10 are factors of 360.
And we knew that X and X-1 are the days.
Therefore X=10.
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