If A is 25% as efficient as B and can complete a certain work taking 15 days more than the time taken by B, in how many days will both A and B together complete the work?4 days5 days7 days10 days
Question
If A is 25% as efficient as B and can complete a certain work taking 15 days more than the time taken by B, in how many days will both A and B together complete the work?4 days5 days7 days10 days
Solution
To solve this problem, we first need to understand the relationship between A and B's efficiency and time taken to complete the work.
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A is 25% as efficient as B. This means that B is 4 times as efficient as A.
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If A takes 15 more days than B to complete the work, we can express A's time as B's time + 15 days.
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Since work is the product of time and efficiency, we can set up the equation: A's time * A's efficiency = B's time * B's efficiency.
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Substituting the given values into the equation, we get: (B's time + 15 days) * 1 = B's time * 4.
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Solving for B's time, we find that B takes 5 days to complete the work.
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If A and B work together, their combined efficiency is 1 + 4 = 5 times the efficiency of A.
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Therefore, the time taken for A and B to complete the work together is the total work divided by their combined efficiency, which is (5 days * 4) / 5 = 4 days.
So, A and B together will complete the work in 4 days.
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