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If A's salary is 37 % more than that of B, then how much percent is B's salary less than that of A (correct to 2 decimal places)?
29.04%
30.86%
29.85%
27.01%
27.01%
If A is x% more than B, then B is less than A by [x / (100 + x)] * 10тБ░%. For x = 37, compute 3700 / 137.
A's salary is 37% more than B's salary.
Percentagedecrease=(100+xxтАЛ)├Ч100
If A is x% more than B, then B is less than A by [x / (100 + x)] * 10тБ░%. For x = 37, compute 3700 / 137.
Many students mistakenly calculate 37% of A's salary and subtract it, ignoring that the base has changed to A's salary.
Define the relationship
Let B's salary be 100. Since A's salary is 37% more than B's, A's salary is 100+37=137.
A=137,B=100
Calculate the difference
The difference between their salaries is AтИТB=137тИТ100=37.
Difference=37
Calculate percentage decrease
To find how much percent B's salary is less than A's, we divide the difference by A's salary and multiply by 100.
Percentage=(13737тАЛ)├Ч100
Final computation
Performing the division 3700├╖137, we get approximately 27.007..., which rounds to 27.01%.
27.007...тЙИ27.01%
D is correct because 37 divided by 137 multiplied by 100 equals approximately 27.01%.
This concept of 'change of base' is frequently tested in Profit & Loss (e.g., mark-up vs margin) and Speed/Time problems.