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UPSC Prelims

CSAT Year Wise (Temporary Link, This will be removed and no PDFs shall be downloaded here. Please download CSAT subject wise files) / सी सैट

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CSAT 2024

Q8 2024, Time and Work

X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?

X, Y और Z एक कार्य को व्यक्तिगत रूप से क्रमशः 6 घंटों, 8 घंटों और 8 घंटों में पूरा कर सकते हैं। यद्यपि, एक ही समय पर प्रत्येक घंटे में केवल एक ही व्यक्ति काम कर सकता है और कोई भी व्यक्ति लगातार दो घंटे काम नहीं कर सकता। सभी को कार्य को पूरा करने में लगाया जाता है। इस कार्य को पूरा करने में उन्हें न्यूनतम कितना समय लगेगा?

Explanation Please wait..

Approach

Find the LCM of 6, 8 and 8, which is 24.
X takes 6 hours to complete the work, so in 1 hour he completes 4 units of work (24 units / 6 hours).
Since Y and Z take 8 hours each to complete the work, in 1 hour they will complete 3 units of work (24 units / 8 hours).
Given, only one person at a time can work in each hour. Nobody can work for two consecutive hours.
To get the the minimum amount of time, we need to utilize X the most because he is most efficient. Hence, every alternative hour, we will utilize X for work.

Now, let's plan their work:

In the first hour, X starts and completes 4 units of work.
In the second hour, Y or Z starts and completes 3 units of work.
In the third hour, X starts again and completes 4 units of work.
In the fourth hour, Y or Z starts and completes 3 units of work.
… And so on.

We need total 24 unit work.

By the above pattern, in 6 hours they will complete 4 + 3 + 4 + 3 + 4 + 3 = 21 units of work.
They have 3 more units of work to complete. X will finish the remaining 3 units of work in 3/4 hours, i.e. 45 minutes.
So, the total time taken is 6 hours + 45 minutes.

Therefore, the correct answer is: (c).

व्याख्या Please wait..

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