GMAT Practice Question: A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment...
Question
A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?
- 16.5 \%
- 20 \%
- 35 \%
- 55 \%
- 65 \%
Topics: word problems, percentages, weighted averages, translations
Solution
Step 1
We first create variables for the beginning-of-year costs
S = \text{salary costs at beginning of 1993} F = \text{fringe-benefit costs at beginning of 1993}
Step 2
We translate the percent increases for each component \textbf{"salary costs rose 3 percent"} and \textbf{"fringe-benefit costs rose 5.5 percent"}
1.03S = S + 0.03S 1.055F = F + 0.055F
Step 3
We translate the overall percent increase \textbf{"employment costs rose 3.5 percent"}
1.035(S + F) = (S + F) + 0.035(S + F)
Step 4
We set the new total cost from components equal to the increased total cost
1.03S + 1.055F = 1.035(S + F)
Step 5
We expand and collect like terms to express fringe-benefit costs in terms of salary costs
1.03S + 1.055F = 1.035S + 1.035F 1.03S - 1.035S + 1.055F - 1.035F = 0 -0.005S + 0.020F = 0 0.020F = 0.005S
Step 6
We find the fraction of total costs represented by fringe benefits
\frac{F}{S} = \frac{0.005}{0.020} = 0.25 \frac{F}{S + F} = \frac{F/S}{S/S + F/S} = \frac{0.25}{1 + 0.25} = \frac{0.25}{1.25} = 0.20 = 20\%
Answer
20%
