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 4days, we have
1x+1x+6=14
⇒(x+6)+xx(x+6)=14
⇒4(2x+6)=x2+6x
⇒8x+24=x2+6x
⇒x2−2x−24=0
⇒x2−6x+4x−24=0
⇒(x−6)(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.