The total price of the machines of a company has gone up by 15%. Cost to install them has also increased from 25% of the cost of total machines to 30% of the cost of total machines.In order to keep the cost same, what should be the percentage reduction in number of machines. Please select the most suitable range in which the calculated percentage lies.00 : 16 : 0613/15 attemptedEndOptions: Pick one correct answer from below16%-17%27%-28%25%-26%23%-24%
Question
The total price of the machines of a company has gone up by 15%. Cost to install them has also increased from 25% of the cost of total machines to 30% of the cost of total machines.In order to keep the cost same, what should be the percentage reduction in number of machines. Please select the most suitable range in which the calculated percentage lies.00 : 16 : 0613/15 attemptedEndOptions: Pick one correct answer from below16%-17%27%-28%25%-26%23%-24%
Solution
Let's break down the problem step by step:
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Let's assume the initial cost of the machines is 100 + 25% of 125.
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Now, the cost of the machines has increased by 15%, so the new cost of the machines is 115 + 30% of 149.5.
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In order to keep the total cost the same as before ($125), we need to find out by what percentage the number of machines should be reduced.
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Let's denote the required reduction percentage as x. So, we have the equation: 125.
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Solving this equation for x gives us x = (149.5 - 125) / 149.5 * 100 = 16.39%.
So, the percentage reduction in the number of machines should be in the range of 16%-17%.
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