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A, B and C can do a piece of work in 3, 12 and 12 days, respectively. How long (in days) will they take to do twice the same work, working together?
Question

A, B and C can do a piece of work in 3, 12 and 12 days, respectively. How long (in days) will they take to do twice the same work, working together?

A.

12

B.

8

C.

5

D.

4

Correct option is D

Given:
Time taken by A = 3 days
Time taken by B = 12 days
Time taken by C = 12 days
Formula Used:
Combined Rate = 1A+1B+1C\frac{1}{A} + \frac{1}{B} + \frac{1}{C}​​

Time taken = Total WorkCombined Rate \frac{Total\ Work}{Combined\ Rate}​​
Solution:
First, let's calculate the 1-day work of each person:
A's 1-day work = 13 \frac{1}{3}​​

B's 1-day work = 112 \frac{1}{12}

C's 1-day work =  112\frac{1}{12}​​
Total 1-day work when they work together:
Rate =  13+112+112\frac{1}{3} + \frac{1}{12} + \frac{1}{12}​​
=412+112+112=612=12= \frac{4}{12} + \frac{1}{12} + \frac{1}{12} = \frac{6}{12} = \frac{1}{2}​​
This means together they complete half the work in 1 day.
Time taken to complete 1 full work = 2 days.
We need to find the time to do twice the same work:
Time required = 2 × 2 = 4 days.
Final Answer
So the correct answer is (d)  

Exam Hall Method:

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