Two numbers are less than a third number by 40% and 47% respectively. The percent by which the second number is less than the first is?Options11.66%5%15%7%
Question
Two numbers are less than a third number by 40% and 47% respectively. The percent by which the second number is less than the first is?Options11.66%5%15%7%
Solution
Let's denote the third number as X.
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The first number is less than X by 40%, so it is 60% of X. We can write this as 0.6X.
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The second number is less than X by 47%, so it is 53% of X. We can write this as 0.53X.
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We are asked to find the percent by which the second number is less than the first. This can be found by subtracting the second number from the first number, dividing by the first number, and then multiplying by 100 to get a percentage.
So, the calculation would be: ((0.6X - 0.53X) / 0.6X) * 100
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Simplifying this gives: (0.07X / 0.6X) * 100
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The X's cancel out, leaving: (0.07 / 0.6) * 100
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Calculating this gives approximately 11.66%
So, the second number is less than the first number by approximately 11.66%.
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