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

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

1. A
10 days
2. B
12 days
3. C
20 days
4. D
5 days

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### Solution:

Let the number of days required for Abu to finish the job be .
Then the number of days required for Babu to finish the job will be .
So, Abu finishes  part of the job and Babu finishes  part of the job in one day.
Given that they can together finish the job in  days, we have
Now taking L.C.M, we get                On simplify the LHS we get,
Now we are doing cross multiply in both the sides
We need to multiply the terms by open brackets
Now taken all the terms in left hand sides and subtract the same degree terms
Thus, we get the equation form. Now we have to factorize the equation.
Here we have to split the terms and we get,
Taking the term as common in first two term and as common on second two term we get
Taking the common term we get
By equating each bracket to zero, we get the roots,                 Time cannot be in negative quantity
Here, is the number of days required for Abu to finish the jobs, so it is not a negative number.
So .
Hence, Abu requires  days and Babu requires days to finish the job alone.
So, option 2 is correct.

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