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If 30% of a number exceeds 20% of it by 12, then the number is:
200
120
150
180
120
Calculate the percentage difference (30%−20%=10%) and equate it to the given difference of 12. So, 10%=12, which means 100%=120.
30% of a number exceeds 20% of the same number by 12.
0.30x−0.20x=12
Calculate the percentage difference (30%−20%=10%) and equate it to the given difference of 12. So, 10%=12, which means 100%=120.
Confusing 'exceeds by' with 'is', or incorrectly setting up the subtraction as 0.20x−0.30x, which results in a negative number.
Define the Variable
Let the number be x.
x
Set up the Equation
The problem states that 30% of x exceeds 20% of x by 12.
0.30x−0.20x=12
Solve the Equation
Subtract the percentages: 0.10x=12. Now divide by 0.10.
x=0.1012=120
B is correct because the difference between 30% and 20% of the number is 10%, which equals 12; therefore, 100% is 120.
This concept of percentage differences is foundational for profit and loss calculations and simple interest problems.
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