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Arithmetic: Time and Work Test-8

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Question 1
Manoj and Ajita can do a job alone in 10 days and 12 days respectively. Manoj starts the work and after 6 days Ajita also joins to finish the work together. For how many days did Ajita actually worked on the job?
Question 1 Explanation: 
For the 6 days work done by Manoj= 6/10 = 3/5
Therefore the remaining work = 1 – 3/5 = 2/5
Now they both can complete the remaining work in 2/5{(10 x 12)/(10+12)}
Now question asks about work done by  Ajita  so Ajita did work for
22/11 days
Question 2
Ashokan is thrice as good a workman as Nitin and is therefore able to finish a piece of work in 40 days  less than Nitin. Find the time in which they can do it working together.
15 days
7 days
16 days
13 days
Question 2 Explanation: 
Let us assume that the work done by Ashokan = w days
So the time taken by Nitin = 3w
So according to the question
3w – w = 40
W = 20 day
And 3w = 60 days
So therefore together they can finish the work in {(20 x 60)/(20 + 60)} = 15days
Question 3
A alone would take 8 more days to complete the job than if both A and B worked together. If B worked alone, he took four and half more days to complete the job than if A and B worked together. How many days would they take if both A and B worked together?
8 days
5 days
2 days
6 days
Question 3 Explanation: 
Let us assume both can complete the work in w days
And we are given the statements that A can complete the work in 8 more days in comparison to when they worked together.
So, we can say that A can complete the work in (w+8) days
In one day, A completes 1/ (w+8) units of work.
Similarly, in one day, B completes 1/(w+4.5) units of work.
Combined work by A and B in one day = {1/ (w+8)} + {1/(w+4.5)}
Now this should be equal to 1/w units of work.
Equating the two,
{1/ (w+8)} + {1/(w+4.5)} = 1/w
We can see that 6 satisfies the above equation.
Thus, option (d) is the correct answer.
Question 4
A can do a piece of work in 40 days. He starts working, but having some other engagements he drops out after 5 days. Thereafter, B completes this work in 21 days. How many days would A and B take to complete this work working together?
16 days
15 days
17 days
11 days
Question 4 Explanation: 
Work done by A in one day = 1/40
Work done by A in five days = 5/40
Therefore the remaining work = 1 – 5/40 = 7/8
So from question we are given that this 7/8 work is done by B in 21 days
Work done by B in one day = 7/8 x 21 = 1/24
Work done by both in one day will be = 1/40 + 1/24 = 1/15
Hence together both would completes the work in 15 days .
Question 5
Madhu takes twice as much time as Uma to complete a work and Ramesh does it in the same time as Madhu and Uma together would. If all three are working together, they can finish the work in 6 days. Then the time taken by Madhu to finish the work is ___?
12 days
14 days
36 days
40 days
Question 5 Explanation: 
We will assume that Madhu can complete the work in 2D days
So Uma can complete the work in D days
So both they can complete the work in {2D x D/2D+D} = 2/3D
Now according to the question we can say that
1/2D + 1/D +3/2D = 1/6
6/2D = 1/6
2D = 36
So Madhu can do the work in 36 days
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