ACT (Enhanced)MathematicsMedium
A civil engineer is calculating the maximum load a bridge can withstand. The stress (S) on a critical component is given by the formula S = k * (L/A), where k is a constant, L is the applied load, and A is the cross-sectional area. If the applied load L is increased by 20% and the cross-sectional area A is decreased by 10%, what is the new stress as a percentage of the original stress?
- A150% of original
- B120% of original
- C108% of original
- D133.3% of original
Show answer & explanationAnswer & explanation
Correct answer: D. 133.3% of original
Let original S = k * (L/A). New L' = 1.20L and New A' = 0.90A. New S' = k * (1.20L / 0.90A) = k * (1.20/0.90) * (L/A) = (1.20/0.90) * S. 1.20 / 0.90 = 12/9 = 4/3 = 1.333... So, New S' ≈ 1.333 * S, which is 133.3% of the original stress.
Why the other options are wrong
- A. This implies a 50% increase, which would occur if the denominator was 0.8, not 0.9.
- B. This only accounts for the increase in L, ignoring the decrease in A.
- C. This is an incorrect calculation, possibly involving addition/subtraction of percentages.
Proportional Change in Formulas
Analyzing how changes in input variables (percentages) affect the output of a formula, especially with multiplicative/divisive relationships.
- Increase by X% means multiplying by (1 + X/100).
- Decrease by X% means multiplying by (1 - X/100).
- Changes multiply when variables are multiplied/divided.
Memory trick: Variable Shift: Convert percentages, substitute, then simplify ratios!