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Question

To complete a job, Babu needs 6 more days than Abu. If both of them do the job together it takes 4 days to complete it. How many days Babu needs, if they do the job separately?

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Solution

Let the number of days required for Abu to finish the job be x.
Then the number of days required for Babu to finish the job will be x+6.

That is, Abu finishes 1x part of the job and Babu finishes 1x+6 part of the job in one day.

Thus, they can together finish 1x+1x+6 part of the job in one day.

Given that they can together finish the job in 4 days, we have

1x+1x+6=14

(x+6)+xx(x+6)=14

4(2x+6)=x2+6x

8x+24=x2+6x

x22x24=0

x26x+4x24=0

(x6)(x+4)=0

x=6 or x=4

Here, x is number of days required for Abu to finish the job, so it is not a negative number.

Thus, x=4 is inadmissible.

Hence, Abu requires 6 days and Babu requires x+6=6+6=12 days to finish the job alone.

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