Question

Two persons A and B together can do a work in 10 days the same work can be finished in 18 days if a working for 12 days and B walk around for 6 days find the time required for each one of them to finish the work if they work alone

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Answer 1

Answer:

Person A would take 15 days alone.

Person B would take 30 days alone.

Step-by-step explanation:

Let a be the fraction of the job that is completed by person A in one day.

Let b be the fraction of the job that is completed by person B in one day.

When they work together, the fraction of the job that they complete in one day is a+b.  As they take 10 days to complete the whole job, this means:

• 10 ( a + b ) = 1

The fraction of the job done by person A in 12 days is 12a, and the fraction of the job done by person B in 6 days is 6b.  Since these two fractions combined result in the whole job being done, this means:

• 12a + 6b = 1

Putting these together gives

• 10 ( a + b ) = 12a + 6b    ⇒    5a + 5b = 6a + 3b    ⇒    a = 2b.

Substituting this into the first equation gives

• 10 ( 2b + b ) = 1    ⇒    30b = 1    ⇒    b = 1 / 30.

Also

• a = 2b = 2 / 30 = 1 / 15.

So person A takes 15 days and person B takes 30 days.

Hope this helps!