EgmatQuantExpert wrote:
3 Deadly Mistakes You Must Avoid in Time and Work Questions – Practice question 3 Leo, Shelly and Raj can complete a certain job in 10, 12, and 15 days respectively. They are assigned to work together to complete the job. All of them started the job together. Leo left 1 day before the completion day and Raj left 2 days before the completion day of the job. In how many days the job gets completed?
A. \(\frac{34}{5}\) days
B. \(\frac{48}{5}\) days
C. \(\frac{57}{12}\) days
D. \(\frac{66}{15}\) days
E. \(\frac{74}{15}\) days
Given data: Leo, Shelly,and Raj can complete a certain job in 10,12,and 15 days.
We assume the work that needs to be done as LCM(10,12,15) = 60 units.
Individual rates are as follows: Leo - 6 units/day | Shelly - 5 units/day | Raj - 4 units/day
If they work together, they will complete 6+5+4 = 15 units in a day. When Raj leaves 2 days before,
Leo & Shelly do 11 units/day. When Leo also leaves work 1 day before, Shelly does 5 units in a day.
Let x be the number of days.
\(15(x-2) + 11 + 5 = 60\) -> \(15x - 30 + 16 = 60\) -> \(15x - 14 = 60\) -> \(x = \frac{74}{15}\) days
Therefore, Leo, Shelly and Raj complete the job in \(\frac{74}{15}\) days
(Option E) _________________
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