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8% of a number is what percentage of 5% of the same number?
160%
150%
125%
140%
160%
Since the number x is common, simply ignore x and calculate the ratio of the percentages directly as (8/5) * 100.
We are given 8% of a number x and 5% of the same number x.
Required┬аPercentage=(WholePartтАЛ)├Ч100
Since the number x is common, simply ignore x and calculate the ratio of the percentages directly as (8/5) * 100.
Students often confuse which value is the base; the phrase 'what percentage OF' indicates the denominator is 5% of the number.
Define the values
Let the number be x. We are comparing 8% of x (which is 0.08x) with 5% of x (which is 0.05x).
V1тАЛ=0.08x,V2тАЛ=0.05x
Set up the percentage ratio
We need to find what percentage V1тАЛ is of V2тАЛ. Applying the formula V2тАЛV1тАЛтАЛ├Ч100.
P=(0.05x0.08xтАЛ)├Ч100
Simplify and Calculate
Cancel x from the numerator and denominator, then solve the fraction 58тАЛ├Ч100.
P=58тАЛ├Ч100=1.6├Ч100=160%
A is correct because the ratio of 8% to 5% is 1.6, which when multiplied by 100 gives 160%.
This concept of relative percentage is the foundation for solving Profit and Loss problems where you compare actual gain/loss against a cost price or a different reference value.