Question : Three people A, B, and C worked together and finished a work in 9 days. If A alone can finish the same work in 18 days, and B alone in 30 days, then the number of days C alone will take is:
Option 1: 36 days
Option 2: 45 days
Option 3: 40 days
Option 4: 54 days
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Correct Answer: 45 days
Solution :
Let
A alone can finish the same work in 18 days.
So 1 day's work of A =
B alone can finish the same work in 30 days.
So 1 day's work of B =
Let C take
When A, B, and C work together, their combined work rate is
The combined work rate of A, B, and C is given by
⇒
⇒
⇒
⇒
⇒
Hence, the correct answer is 45 days.
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