Mahesh and Umesh can complete a work in 10 days and 15 days respectively. Umesh starts the work and after 5 days Mahesh also joins him. In all, the work would be completed ina)7 daysb)9 daysc)11 daysd)12 dayse)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Umesh 5 days work =5/15;
remaining work =1-1/3=2/3;
together 1 day work of Mahesh and Umesh = 1/15+1/10= 1/6;
so, they will do together 2/3 of work in =(2/3)/+(1/6) =4 days.
hence, the work was completed in (4+5) =9 days. op(b)

Answer

Given data:
Mahesh can complete work in 10 days
Umesh can complete work in 15 days

Let's assume the total work to be done is 'x'
So, the work done by Umesh in one day = x/15
And the work done by Mahesh in one day = x/10

Umesh starts the work and works for 5 days, so the work done by Umesh in 5 days = 5(x/15) = x/3
Now, the remaining work = x - x/3 = 2x/3

Now, both Umesh and Mahesh work together on remaining work = 2x/3
Let's assume that they take 'n' days to complete the remaining work together.
So, the work done by Umesh in 'n' days = n(x/15)
And the work done by Mahesh in 'n' days = n(x/10)

Total work done in 'n' days = n(x/15) + n(x/10) = (2nx/30) + (3nx/30) = 5nx/30 = nx/6

According to the question, the total number of days taken to complete the work together is 9 days.
So, the work done by Umesh in 5 days + the work done by both Umesh and Mahesh in 9 days = x
x/3 + nx/6 = x
n/2 + 1 = 2
n/2 = 1
n = 2

So, the remaining work will be completed by both Umesh and Mahesh in 2 days.
Therefore, the total number of days taken to complete the work = 5 (days taken by Umesh) + 2 (days taken by both Umesh and Mahesh) = 7 days.

Hence, the correct answer is option B) 7 days.

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