EgmatQuantExpert wrote:
3 Deadly Mistakes You Must Avoid in Time and Work Questions – Practice question 4 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, and Raj left 2 days before the original scheduled 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
Leo – 10 days
Shelly – 12 days
Raj – 15 days.
The trick is take the LCM or any comman multiple of the number of days and assume it the work to be done. In this case –
I choose 120 So let say work is 120 unit. If you want you can choose 60 as well which is LCM of 10, 12, 15.
Now Leo alone will be able to do 120 units in 10 days and per day he will do 12 units of work
Shelly alone will be able to do 120 units in 12 days and per day she will do 10 units of work
Raj alone will be able to do 120 units in 15 days and per day he will do 8 units of work
Now if they start working together – work will be finished in 4day. How? 120/(12+10+8)
Leo left 1 day before the completion that means he was there for 3days. He must have performed 36 units.
Raj left 2 days before the completion that means he was there for 2 days. He must have done 16 units.
Note all three were there for 2days so 60 units of work is done.
For 3rd day only Leo and Shelly work – units of work they will complete together – 22 units ( 10 + 12).
Total work complete – 60 +22 = 82Units.
On fourth day, Shelly will be alone and work left = 38 Units. For this to complete she will need 38/10 days.
Total No. of days = 3 + 38/10 = 34/5 days.