A can do a work in 36 days and B in 32 days. If they work on it together for 12 days, then what fraction of work is left?Options7/24134557/7211933
Question
A can do a work in 36 days and B in 32 days. If they work on it together for 12 days, then what fraction of work is left?
Options:
- 7/24
- 1345
- 57/72
- 11933
Solution
Sure, let's solve this step by step:
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First, we need to find out how much work A and B can do in a day. A can finish the work in 36 days, so A can do 1/36 of the work in a day. B can finish the work in 32 days, so B can do 1/32 of the work in a day.
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If they work together, we can add up the work they can do in a day. So, A and B together can do (1/36 + 1/32) of the work in a day.
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To simplify this, find a common denominator for 36 and 32, which is 288. So, A and B together can do (8/288 + 9/288) = 17/288 of the work in a day.
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If they work together for 12 days, they can do (17/288 * 12) = 204/288 = 0.708333 of the work.
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Since the total work is 1, the fraction of work left is (1 - 0.708333) = 0.291667.
So, the fraction of work left is approximately 7/24 when rounded to the nearest whole number in the denominator. Therefore, the answer is 7/24.
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