Question

Ramu can complete a job in 8 days, Shyamu can complete the same job in 12 days. However, Monu takes 12 days to complete \[{\dfrac{3}{4}^{th}}\] of the same job. Ramu works for 2 days and then leaves the job. The number of days that will be taken by Shaymu and Monu to balance together is
A. 4.2
B. 5.1
C. 6.2
D. 6.5

Answer 1

Hint: Let us find the job by Ramu, Shyamu and Monu separately in one day, and also find the job that has to be done by Shyamu and Monu together.

Complete Step-by-Step solution:
As we know that Ramu completes a job in 8 days. So, Ramu one day job will be = \[\dfrac{1}{8}\]
Shyamu completed the same job in 12 days. So, Shyamu one day job will be = \[\dfrac{1}{{12}}\]
Now Monu takes 12 days to complete \[{\dfrac{3}{4}^{th}}\] of the same job.
So, the number of days taken by Monu to complete the job will be = \[\dfrac{4}{3} \times 12 = 16\] days.
So, Monu one day job will be = \[\dfrac{1}{{16}}\]
Now it is given in the question that Ramu works for two days and then leaves the job.
So, job done by Ramu in 2 days will be equal to 2 * job done by Ramu in one day.
So, job done by Ramu = 2\[ \times \] \[\dfrac{1}{8}\] = \[\dfrac{1}{4}\]
So, now the left job will be equal to 1 – \[\dfrac{1}{4}\] = \[\dfrac{3}{4}\]
Now as we know that the left \[\dfrac{3}{4}\] of the job should be done by Monu and Shyamu.
So, a job done by Monu and Shyamu in one day will be equal to the summation of a job done by Monu and Shyamu separately in one day.
So, job done by Monu and Shyamu in one day will be = \[\dfrac{1}{{12}} + \dfrac{1}{{16}} = \dfrac{{16 + 12}}{{12 \times 16}} = \dfrac{{28}}{{192}} = \dfrac{7}{{48}}\]
Now time taken by Monu and Shyamu to complete the job will be equal to the total job left divided by the job done by Monu and Shyamu in one day .
So, time taken by Monu and Shyamu to complete the rest of the job will be = \[\dfrac{{\dfrac{3}{4}}}{{\dfrac{7}{{48}}}} = \dfrac{3}{4} \times \dfrac{{48}}{7} = \dfrac{{3 \times 12}}{7} = \dfrac{{36}}{7} \approx 5.1\] days
So, the time taken by Monu and Shyamu to complete the rest of the job will be equal to 5.1 days.
Hence, the correct option will be B.

Note: Whenever we come up with this type of problem then first, we have to find the job done by each person in one day separately. After that we had to find the job done by Ramu in 2 days and then subtract that with 1 to get the job left for Shyamu and Monu . And then we add the job done by Shyamu and Monu separately to get the job done by them in one day if they work together. Now to find the time taken by Monu and Shyamu to complete the rest of the job will be equal to the total job left divided by the job done by Monu and Shyamu in one day.