P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?a)60/11b)31/11c)71/11d)72/11Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Let's first calculate the work done by P and Q individually.

P can complete the work in 12 days working 8 hours a day, so the work done by P in one day is:
1/12 * 8 = 2/3

Q can complete the work in 8 days working 10 hours a day, so the work done by Q in one day is:
1/8 * 10 = 5/4

Now, let's calculate the combined work done by P and Q working together.

Since P and Q are working together for 8 hours a day, the combined work done by P and Q in one day is:
2/3 + 5/4 = (8 * 2 + 5 * 3) / (3 * 4) = 16/12 + 15/12 = 31/12

Therefore, P and Q together can complete 31/12 of the work in one day.

Now, let's calculate the number of days required for P and Q to complete the entire work.

Let the number of days required be x.

Since P and Q together can complete 31/12 of the work in one day, the total work done by P and Q in x days is:
(31/12) * x

According to the question, P and Q together can complete the entire work in x days, so:

(31/12) * x = 1

Simplifying the equation, we get:
x = 12/31

So, P and Q together can complete the work in 12/31 days.

Now, let's simplify the answer.

12/31 = 60/155 = 60/11 * 1/14 = 60/11 * 2/28 = (60 * 2) / (11 * 28) = 120/308 = 60/154 = 60/11

Therefore, P and Q together can complete the work in 60/11 days.

Hence, the correct answer is option A) 60/11.

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