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

Step 1: Write the combined rates of each pair.
Stuart + Jack \(= \frac{1}{10}\) work per day. Jack + Leo \(= \frac{1}{15}\) work per day. Stuart + Leo \(= \frac{1}{12}\) work per day.
Step 2: Add all three equations.
Adding the three pair rates counts each person's rate exactly twice: \(2(S+J+L) = \frac{1}{10} + \frac{1}{15} + \frac{1}{12}\). Using LCM 60: \(\frac{6}{60} + \frac{4}{60} + \frac{5}{60} = \frac{15}{60} = \frac{1}{4}\).
Step 3: Find the combined rate of all three.
\(S + J + L = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}\) work per day.
Step 4: Find the work done in the first 2 days.
All three work together for 2 days: work done \(= 2 \times \frac{1}{8} = \frac{1}{4}\).
Step 5: Find the remaining work.
Remaining work \(= 1 - \frac{1}{4} = \frac{3}{4}\).
Step 6: Find the time for Stuart and Jack to finish the remaining work.
Stuart and Jack work at rate \(\frac{1}{10}\) per day, so time \(= \frac{3/4}{1/10} = \frac{3}{4} \times 10 = 7.5\) days.
Step 7: Rule out the other options.
Options 1 (9), 2 (12) and 3 (8) do not match this exact calculation of remaining work divided by the Stuart-Jack rate. Only 7.5 days is correct.