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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:
A's time = 3 days
B's time = 12 days
C's time = 12 days
Target Work = Twice the original work
Formula Used:
Total Work = LCM of individual times
Time = Total WorkCombined Efficiency \frac{Total\ Work}{Combined\ Efficiency}​​
Solution:
Let the original total work be the LCM of 3, 12, and 12, which is 12 units.
Efficiency of A = 123\frac{12}{3}​ = 4 units/day

Efficiency of B = 1212\frac{12}{12}​ = 1 unit/day

Efficiency of C = 1212 \frac{12}{12}​ = 1 unit/day

Combined efficiency = 4 + 1 + 1 = 6 units/day
Target work is twice the original = 2 × 12 = 24 units.
Time required = 246\frac{24}{6}​ = 4 days
Final Answer
So the correct answer is (d)

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