CSAT 2024 Solutions - X, Y, and Z can complete a piece of work individually in 6 hours, 8 hours, and 8 hours respectively.

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A. 6 hours 15 minutes
B. 6 hours 30 minutes
C. 6 hours 45 minutes
D. 7 hours

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Answer: C. 6 hours 45 minutes

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Explanation:

X, Y, and Z can complete the work individually in 6 hours, 8 hours, and 8 hours, respectively. To minimize the total time required to finish the work, we need to utilize the most efficient worker, X, as much as possible. Thus, we will alternate between X and either Y or Z, starting with X.

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**Work Rates:**

• X completes the work in 6 hours, so in one hour, X completes 1/6 of the work.
• Y (or Z) completes the work in 8 hours, so in one hour, Y (or Z) completes 1/8 of the work.

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**Work Distribution:**

We will alternate between X and Y (or Z) in the following pattern:

• First hour: X works, completing 1/6 of the work.
• Second hour: Y (or Z) works, completing 1/8 of the work.
• Third hour: X works, completing 1/6 of the work.
• Fourth hour: Y (or Z) works, completing 1/8 of the work.
• Fifth hour: X works, completing 1/6 of the work.

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After 6 hours, the total work completed is: 

3X + 3Y = 3 × 1/6 + 3 × 1/8 = 1/2 + 3/8 = 7/8

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**Remaining Work:**

After 6 hours, 7/8 of the work is completed, leaving 1/8 of the work remaining. Since it’s now X’s turn to work, we calculate how much time X will need to complete the remaining 1/8 of the work:

• X completes 1/6 of the work in 1 hour,
• So to complete 1/8, the time required is: (1/8 ÷ 1/6) hours = 3/4 hours = 3/4 × 60 minutes = 45 minutes

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**Total Time:** Thus, the total time to complete the work is:

6 hours (for the first 7/8 of the work) + 45 minutes (for the remaining 1/8) = 6 hours 45 minutes.

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Thus, the correct answer is **C. 6 hours 45 minutes**.

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