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Two numbers are respectively 30% and 37% less than a third number. What percentage of the first number is the second number?
10%
80%
90%
20%
90%
Assume the third number is 100. Then the first two numbers are (100-30)=70 and (100-37)=63. The required percentage is simply (63/70) * 100.
Two numbers are 30% and 37% less than a third number.
Percentage=ValueBтАЛValueAтАЛтАЛ├Ч100
Assume the third number is 100. Then the first two numbers are (100-30)=70 and (100-37)=63. The required percentage is simply (63/70) * 100.
Students often calculate the percentage difference (7%) instead of the ratio of the second number to the first number.
Assume the third number
Let the third number be 100.
Third┬аNumber=100
Calculate the first and second numbers
The first number is 30% less than 100, which is 100тИТ30=70. The second number is 37% less than 100, which is 100тИТ37=63.
Number1тАЛ=70,Number2тАЛ=63
Find the required percentage
The question asks what percentage of the first number (70) is the second number (63).
Percentage=7063тАЛ├Ч100
Final calculation
Simplifying the fraction: 7063тАЛ=109тАЛ. Multiplying by 100 gives 90%.
0.9├Ч100=90%
C is correct because the ratio of the second number (63) to the first number (70) multiplied by 100 equals 90%.
This method of assuming 100 is highly effective for any problem involving multiple percentages relative to a single base value in data interpretation and arithmetic sections.