Question : A is twice as good a workman as B and B is twice as good a workman as C. If A and B can together finish a piece of work in 4 days, then C can do it by himself in:
Option 1: 6 days
Option 2: 8 days
Option 3: 24 days
Option 4: 12 days
Correct Answer: 24 days
Solution :
Let A can do the whole work in 1 day, B in 2 days, and C in 4 days.
LCM of 1, 2 and 4 is 4
Efficiency of A = $\frac{4}{1}$ = 4 units
Efficiency of B = $\frac{4}{2}$ = 2 units
Efficiency of C = $\frac{4}{4}$ = 1 units
Efficiency of both (A + B) = 4 + 2 = 6 units
Total work = Efficiency × Time = 6 × 4 = 24 units
$\therefore$ Total work can be completed by C alone = $\frac{24}{1}$ = 24 days
Hence, the correct answer is 24 days.
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