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Two numbers are less than a third number by 30% and 37%, respectively. By what percentage is the second number less than the first?
15%
8%
12%
10%
10%
Assume the third number is 100. Then the first number is 70 and the second number is 63. Calculate the percentage reduction from 70 to 63.
Two numbers are 30% and 37% less than a third number.
Percentage┬аDifference=Base┬аValueDifferenceтАЛ├Ч100
Assume the third number is 100. Then the first number is 70 and the second number is 63. Calculate the percentage reduction from 70 to 63.
Many students mistakenly divide the difference by the third number (100) instead of the first number (70), resulting in an incorrect answer of 7%.
Assume the base value
Let the third number be 100. The first number is 30% less than 100, so First Number = 100тИТ30=70.
N3тАЛ=100,N1тАЛ=70
Determine the second number
The second number is 37% less than 100, so Second Number = 100тИТ37=63.
N2тАЛ=63
Calculate the percentage difference
We need to find by what percentage the second number (63) is less than the first number (70). The difference is 70тИТ63=7.
Percentage=7070тИТ63тАЛ├Ч100
Final calculation
Calculating the final percentage: 707тАЛ├Ч100=0.1├Ч100=10%.
Percentage=10%
D is correct because the percentage decrease from the first number (70) to the second number (63) is exactly 10%.
This concept of 'base value' is crucial in Profit & Loss problems as well, where profit is always calculated on the Cost Price, not the Selling Price.