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

Answer 1

The Correct Option is D

To solve this problem, let's denote the work done by Stuart, Jack, and Leo per day as \( S \), \( J \), and \( L \) respectively. We have three equations based on the given information:

• Stuart and Jack: \( S + J = \frac{1}{10} \)
• Jack and Leo: \( J + L = \frac{1}{15} \)
• Stuart and Leo: \( S + L = \frac{1}{12} \)

We want to find the combined work rate of Stuart and Jack to compute how long they take to finish the remaining work. First, add the three equations:

\((S + J) + (J + L) + (S + L) = \frac{1}{10} + \frac{1}{15} + \frac{1}{12}\)

Which simplifies to:

\(2S + 2J + 2L = \frac{1}{10} + \frac{1}{15} + \frac{1}{12}\)

Combine like terms:

\(2(S + J + L) = \frac{1}{10} + \frac{1}{15} + \frac{1}{12}\)

Find a common denominator (60):

\(2(S + J + L) = \frac{6}{60} + \frac{4}{60} + \frac{5}{60} = \frac{15}{60} = \frac{1}{4}\)

\((S + J + L) = \frac{1}{8}\)

Now knowing the combined rate of all three, calculate \( S + J \):

\(S + J = (S + J + L) - L = \frac{1}{8} - L\)

From the equation \( J + L = \frac{1}{15} \), solve for \( L \):

\(L = \frac{1}{15} - J\)

Substitute \( L \) in the equation \( S + L = \frac{1}{12} \) to solve:

\(S + \left(\frac{1}{15} - J\right) = \frac{1}{12}\)

Simplify and solve for \( J \) and substitute back for \( S + J \). But realizing the complexity of simplifying directly, observe they worked together for 2 days, leaving:

Work done in 2 days: \(2 \times \frac{1}{8} = \frac{1}{4}\)

Remaining work: \(1 - \frac{1}{4} = \frac{3}{4}\)

Stuart and Jack's combined rate: \(S + J = \frac{1}{10}\)

Time required for the remaining work:

\(\text{Time} = \frac{\text{Remaining work}}{\text{Combined rate}} = \frac{3/4}{1/10} = \frac{3/4} \times \frac{10}{1} = 7.5\)

Thus, Stuart and Jack will take 7.5 days to finish the rest of the work.