X can do 60% of a task in 15 days. Efficiency of Y is 25% more than that of X. Both X and Y started working together and left the task after four days. Z completed the remaining task in 24 days. Efficiency of Z is what percent more/less than that of X?1) 20% more2) 25% more3) 50% less4) 33.33% les
Question
X can do 60% of a task in 15 days. Efficiency of Y is 25% more than that of X. Both X and Y started working together and left the task after four days. Z completed the remaining task in 24 days. Efficiency of Z is what percent more/less than that of X?1) 20% more2) 25% more3) 50% less4) 33.33% les
Solution
Let's break down the problem step by step:
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X can do 60% of a task in 15 days. This means X can complete the entire task in 15 / 0.6 = 25 days.
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The efficiency of X is therefore 1/25 = 0.04 of the task per day.
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Y's efficiency is 25% more than X's, so Y's efficiency is 0.04 * 1.25 = 0.05 of the task per day.
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Together, X and Y can do 0.04 + 0.05 = 0.09 of the task per day. In 4 days, they complete 4 * 0.09 = 0.36 or 36% of the task.
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This leaves 1 - 0.36 = 0.64 or 64% of the task for Z, which Z completes in 24 days. Therefore, Z's efficiency is 0.64 / 24 = 0.02667 of the task per day.
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To find out how much more or less efficient Z is than X, we calculate the difference between their efficiencies: 0.02667 - 0.04 = -0.01333.
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We then divide this difference by X's efficiency and multiply by 100 to get the percentage: (-0.01333 / 0.04) * 100 = -33.33%.
So, Z's efficiency is 33.33% less than X's. The answer is 4) 33.33% less.
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