B is twice as efficient as A and A can do a piece of work in 21 days. A started the work and after a few days B joined him. They completed the work in 15 days from starting. For how many days did they work together?Select one:a. 2 daysb. 3 daysc. 6 1/2 daysd. 5 dayse. 6 days
Question
B is twice as efficient as A and A can do a piece of work in 21 days. A started the work and after a few days B joined him. They completed the work in 15 days from starting. For how many days did they work together?Select one:a. 2 daysb. 3 daysc. 6 1/2 daysd. 5 dayse. 6 days
Solution
Let's solve this step by step:
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We know that A can complete the work in 21 days. So, A's work rate is 1/21 of the work per day.
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B is twice as efficient as A, so B's work rate is 2/21 of the work per day.
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Together, A and B can do (1/21 + 2/21) = 3/21 of the work per day.
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We know that A and B together finished the work in 15 days. So, in those 15 days, they did 15 * (3/21) = 45/21 = 15/7 of the work.
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This means that A alone did the rest of the work, which is 1 - 15/7 = 2/7 of the work.
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Since A's work rate is 1/21 of the work per day, A worked alone for (2/7) / (1/21) = 6 days.
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Therefore, A and B worked together for 15 - 6 = 9 days.
So, the answer is not in the options given. There might be a mistake in the question or the options.
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