Exercise: Ratio & Proportion
Questions for: Distribution and Comparison
A company distributes its annual bonus among three teams – Alpha, Beta, and Gamma – in the ratio 3:5:2. The total bonus allocated for the year is $120,000. Team Beta then shares its portion equally among its 20 members, while Team Gamma shares its portion equally among its 10 members.
What is the difference in the bonus received by an individual member of Team Beta compared to an individual member of Team Gamma?
A: $600
B: $1,200
C: $2,400
D: $3,000
Answer: A
1. Determine the total number of ratio parts: 3 + 5 + 2 = 10 parts.
2. Calculate the value of one ratio part: $120,000 / 10 = $12,000.
3. Calculate Team Beta's total bonus: 5 parts * $12,000/part = $60,000.
4. Calculate Team Gamma's total bonus: 2 parts * $12,000/part = $24,000.
5. Calculate the bonus per individual member in Team Beta: $60,000 / 20 members = $3,000 per member.
6. Calculate the bonus per individual member in Team Gamma: $24,000 / 10 members = $2,400 per member.
7. Calculate the difference: $3,000 - $2,400 = $600.
Why others are wrong:
A — Correct answer.
B — This value might result from miscalculations, such as incorrect division of a total share or an error in calculating individual portions.
C — This is the individual bonus received by a Team Gamma member only, not the requested difference.
D — This is the individual bonus received by a Team Beta member only, not the requested difference.
Alex, Ben, and Chloe received a $900 prize for their collaborative project. They decided to distribute the prize money among themselves in the ratio of 2:3:4, based on their individual contributions, with Alex receiving the first share, Ben the second, and Chloe the third.
What is the difference in the amount of prize money received by Chloe and Alex?
A: $200
B: $100
C: $300
D: What is the difference in the amount of prize money received by Chloe and Alex?
A. $200
B. $100
C. $300
D. $400
Answer: A
1. Sum the ratio parts: 2 + 3 + 4 = 9 total parts.
2. Calculate the value of one ratio part: $900 (total prize) / 9 parts = $100 per part.
3. Calculate Alex's share: 2 parts * $100/part = $200.
4. Calculate Chloe's share: 4 parts * $100/part = $400.
5. Find the difference between Chloe's and Alex's shares: $400 - $200 = $200.
Why others are wrong:
A — Correct.
B — This represents the value of one ratio part, or the difference between adjacent shares (e.g., Ben's and Alex's, or Chloe's and Ben's).
C — This is Ben's share of the prize money (3 parts * $100 = $300).
D — This is Chloe's total share of the prize money.
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