Question:
A and B together can complete a work in 12 days, B and C together in 15 days, and C and A together in 20 days. In how many days can A alone complete the work?
A and B together can complete a work in 12 days, B and C together in 15 days, and C and A together in 20 days. In how many days can A alone complete the work?
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For work-rate problems, sum pairwise rates and subtract to find individual rates.
Updated On: Jul 24, 2025
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The Correct Option is B
Solution and Explanation
Let A, B, C’s work rates be \( a, b, c \) (work/day).
Given: \( a + b = \frac{1}{12}, b + c = \frac{1}{15}, c + a = \frac{1}{20} \).
Add all:
\[ 2(a + b + c) = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5 + 4 + 3}{60} = \frac{12}{60} = \frac{1}{5} \] \[ a + b + c = \frac{1}{10} \] \[ a = (a + b + c) - (b + c) = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30} \] Time for A alone = \( \frac{1}{\frac{1}{30}} = 30 \) days.
Thus, the answer is 30.
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