Question

Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave and then Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?
A. 6 days
B. 8 days
C. 10 days
D. 11 days
E. 12 days

Answer 1

Hint: We are given the 4 days of work done by Ram and Shyam both. Letting the complete work done be 1 unit and subtracting Shyam`s 8 days of work done from it we can get the work done by Shyam alone. Then we can easily find the work done by Shyam in one day and then proceed further.

Complete answer:
Let the work done by Ram and Shyam be R and S respectively.
Given, (R&S)’s 4 days’ work = 60/100 of work
(R&s)’s 1-day work = \[ = \dfrac{{60}}{{100}} \times \dfrac{1}{4} = \dfrac{{15}}{{100}}\] of work
After ram takes leave:
S’s 8 days of work \[ = \left( {1 - \dfrac{{60}}{{100}}} \right) = \dfrac{{40}}{{100}}\] of work
S’s one day of work \[ = \dfrac{{40}}{{100}} \times \dfrac{1}{8} = \dfrac{5}{{100}}\] of work
So, Ram’s 1-day work = (R+S)’s 1-day work – S’s 1-day work
\[ = \left( {\dfrac{{15}}{{100}} - \dfrac{5}{{100}}} \right)\] of work
\[ = \dfrac{1}{{10}}\] of work
So, Ram will take 10 days to complete the entire job alone.
Therefore, the correct option is C. 10 days

Note: Here the number of days in which work done by Ram alone cannot be less than the number of days in which Both Ram and Shyam have done the work completely. And the same will apply to the number of days in which work done by Shyam alone. In questions like these, work done is calculated in fraction, this fraction is actually the reciprocal of no. of days in which work is done. So, the denominator of the fraction stands for the no. of days.