I totally agree with the explanations given above. Just thought of giving another approach by using the answer choices.
If you analyze the answer choices, Did you notice something interesting?
A = 24 days is common in all answer choices.
My next question is can we use it to solve the question? Yes. you can.
we can confirm that A will take 24 days to finish the work alone. Using this data will help you to save some time.
LCM approach is more convenient here. Lets assume the total work = LCM ( 72,12,24) = 72 units.
Since we are asked to calculate the time taken by A, B, and C to finish the work alone, we need to calculate the individual rate of A, B and C respectively.
By using the data from answer choices, we can easily find the rate of A.
Rate of A = 72/24 = 3 units / day . As A can complete the work in 24 days working alone.
Rate of A and B = 72/(72/5) = 5 units/day
Rate of B = 5 - 3 = 2 units/day
Rate of B and C = 72/12 = 6 units /day.
Rate of C = 6 - 2 = 4 units /day
Since we know the individual rates of B and C, it's very easy to calculate the time taken by each of them to complete the work alone.
Time taken by B alone = Total work / Rate of B = 72/2 = 36 days
Time taken by C alone = Total work / Rate of C = 72/4 = 18 days.
Option A is the answer.Remember, you can always use the answer choices to your advantage.
Thanks,
Clifin J Francis,
GMAT QUANT SME
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