Question

Ramesh can complete a work in 20 days. Mohan is 66.67% as efficient as Ramesh. Mohan and Ramesh work
together. Ramesh leaves after working for some days. The remaining work is done by Mohan in 10 days. After
how many days did Ramesh leave the work?
Options : A : 10, B: 6.5, C:8.5, D: 8

Answer 1

Answer:

Option D

Step-by-step explanation:

Mohan can complete work in 30 days. In 10 days Mohan would have completed one third of the work. Remaining work would be 2/3. Ramesh and Mohan can do 1/12 work per day. 2/3 work would be completed in 8 days if they work together.

Answer 2

Answer:

After 8 days Ramesh left work.

Step-by-step explanation:

Given:

Ramesh completes work in 20 days

Let the Total work to be completed = 1 (1 unit)

So,

Ramesh can complete (1/20) part of the work in 1 day

Given that-

Mohan is 66.67% as efficient as Ramesh

i.e., If Ramesh completes X part of work in 1 day, then Mohan completes $\frac{2X}{3}$ part of work in 1 day.

Here, Ramesh completes$(\frac{1}{20})$ part of the work in 1 day

So, Mohan can complete $(\frac{2}{3})*(\frac{1}{20}) = (\frac{1}{30})$ part of the work in 1 day

Mohan can complete work in 30 days

Let D be the days Ramesh has worked i.e., after D days Ramesh left the work.

Both Ramesh and Mohan can complete $(\frac{1}{20}+\frac{1}{30})$ part of the work in 1 day.

In D days Ramesh and Mohan can complete  $D\times (\frac{1}{20}+\frac{1}{30})$ part of the work

In 10 days Mohan can complete

10*(1/30) part of work

We have,

              $D(\frac{1}{20}+\frac{1}{30}) + 10(\frac{1}{30}) = 1$

L.C.M of (20,30) = 60

D(3+2) + 10 x 2 = 60

5D + 20 = 60

5D = 40

D = 8

Therefore, After 8 days Ramesh left work.

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