Question

Stuart, Jack and Leo are colleagues working in a plant. Stuart and Jack can do a work in 10 days, Jack and Leo can do the same work in 15 days while Stuart and Leo can do it in 12 days. All of them started the work together. After two days, Leo was shifted to some other work. How many days will Stuart and Jack take to finish the rest of the work?

• A. 9
• B. 12
• C. 8
• D. 7.5

Hint:

Add all three pairwise rates to get twice the combined rate of all three, subtract the two-day work done, then divide by Stuart and Jack's rate.

Answer 1

The Correct Option is D

This can also be solved using the LCM-of-work (unit work) method instead of fractional rates.
Let the total work be 120 units, the LCM of 10, 15 and 12.
Stuart + Jack rate = $\frac{120}{10} = 12$ units per day.
Jack + Leo rate = $\frac{120}{15} = 8$ units per day.
Stuart + Leo rate = $\frac{120}{12} = 10$ units per day.
Adding all three pair rates: $12 + 8 + 10 = 30$ units per day, which equals $2(S+J+L)$.
So the combined rate of all three together is $S+J+L = \frac{30}{2} = 15$ units per day.
In the first 2 days, all three working together complete $2 \times 15 = 30$ units.
Remaining work = $120 - 30 = 90$ units.
After Leo leaves, only Stuart and Jack work, at their known combined rate of 12 units per day.
Time to finish the remaining 90 units = $\frac{90}{12} = 7.5$ days.\[\boxed{7.5 \text{ days}}\]