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If x% of 600 = 12% of 250 + 18% of 300, then the value of x is:
18
12
14
16
18
Use the property of common percentages: 12% of 250 is the same as 6% of 500 (halving one, doubling other), and then factor out terms to simplify the division by 600 quickly.
x% of 600 = 12% of 250 + 18% of 300
100x×600=10012×250+10018×300
Use the property of common percentages: 12% of 250 is the same as 6% of 500 (halving one, doubling other), and then factor out terms to simplify the division by 600 quickly.
Students often calculate the right side incorrectly by failing to convert percentage to fractions (e.g., writing 0.12 instead of 12/100) or by making arithmetic errors in simple multiplication.
Set up the equation
Translate the words into a mathematical equation.
100x×600=(10012×250)+(10018×300)
Simplify both sides
Cancel the zeros and simplify the products on the right side.
6x=(12×2.5)+(18×3)⟹6x=30+54
Solve for x
Sum the values on the right and divide by 6.
6x=84⟹x=684=14
C is correct because the calculation 6x=30+54 leads to 6x=84, and 84/6=14.
This type of simplification is fundamental for Data Interpretation (DI) sets where you often need to find the sum of percentage-based values within large tables.
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