Exercise: Ratio & Proportion
Questions for: Distribution and Comparison
A multi-national corporation has three core departments: Research, Development, and Support. The corporation employs a total of 350 people across these departments. The number of employees in Research to Development is in the ratio 2:3, and the number of employees in Development to Support is in the ratio 4:5.
How many more employees are in the Support department than in the Research department?
A: 60
B: 70
C: 80
D: 90
Answer: B
1. First, combine the two ratios R:D = 2:3 and D:S = 4:5. To do this, find a common multiple for the Development (D) part, which is 12 (LCM of 3 and 4).
2. Multiply the R:D ratio by 4: (2*4) : (3*4) = 8:12.
3. Multiply the D:S ratio by 3: (4*3) : (5*3) = 12:15.
4. The combined ratio R:D:S is 8:12:15.
5. Calculate the total number of parts in the combined ratio: 8 + 12 + 15 = 35 parts.
6. Determine the value of one ratio part by dividing the total number of employees by the total parts: 350 employees / 35 parts = 10 employees per part.
7. Calculate the number of employees in Research (R) and Support (S):
* Research (R) = 8 parts * 10 employees/part = 80 employees.
* Support (S) = 15 parts * 10 employees/part = 150 employees.
8. Find the difference between the number of employees in the Support department and the Research department: 150 - 80 = 70.
Why others are wrong:
A — This could result from an incorrect calculation of one of the departments or an arithmetic error in the final subtraction (e.g., if Research was 90, then 150-90=60).
C — This is the number of employees in the Research department, not the difference.
D — This would be the result if Research was incorrectly calculated as 60 employees (150-60=90), or a general arithmetic error.
A company allocated a total bonus of $12,000 to be distributed among three top-performing employees: Sarah, Mark, and Emily. The distribution was based on their performance scores, in the ratio 3:4:5 respectively.
How much more did Emily receive compared to Sarah?
A: $1,000
B: $2,000
C: $3,000
D: $4,000
Answer: B
1. Sum the ratio parts to find the total number of shares: 3 + 4 + 5 = 12 parts.
2. Determine the value of one ratio part by dividing the total bonus by the total parts: $12,000 / 12 = $1,000 per part.
3. Calculate Sarah's bonus: 3 parts * $1,000/part = $3,000.
4. Calculate Emily's bonus: 5 parts * $1,000/part = $5,000.
5. Find the difference between Emily's and Sarah's bonus: $5,000 - $3,000 = $2,000.
Why others are wrong:
A — This represents the value of one ratio part.
B — Correct.
C — This represents Sarah's total bonus amount.
D — This represents Mark's total bonus amount.
Discuss About this Question.
A company allocated a total bonus of $120,000 to its Sales, Marketing, and R&D departments in the ratio 3:2:1, respectively. Following an exceptional quarter for product innovation, the R&D department received an additional $25,000.
By what percentage is R&D's final bonus larger than Marketing's bonus?
A: 10%
B: 12.5%
C: 15%
D: 20%
Answer: B
1. Calculate the value of one ratio part: Total bonus / Sum of ratio parts = $120,000 / (3+2+1) = $120,000 / 6 = $20,000.
2. Determine Marketing's bonus: 2 parts * $20,000/part = $40,000. This is Marketing's final bonus as it received no additional allocation.
3. Determine R&D's initial bonus: 1 part * $20,000/part = $20,000.
4. Calculate R&D's final bonus: Initial bonus + Additional allocation = $20,000 + $25,000 = $45,000.
5. Find the difference between R&D's final bonus and Marketing's bonus: $45,000 - $40,000 = $5,000.
6. Calculate the percentage difference relative to Marketing's bonus: ($5,000 / $40,000) * 100% = 0.125 * 100% = 12.5%.
Why others are wrong:
A — Results from an arithmetic error or using an incorrect base for the percentage calculation.
C — Results from an arithmetic error or using an incorrect base for the percentage calculation.
D — Results from an arithmetic error or using an incorrect base for the percentage calculation.
Discuss About this Question.
A company allocates an annual bonus of $120,000 across three departments: Sales, Marketing, and Operations, in a ratio of 3:2:1, respectively. The Marketing department then distributes its entire allocated bonus equally among its 5 team leaders.
What is the difference between the total bonus received by the Operations department and the amount received by a single Marketing team leader?
A: $12,000
B: $8,000
C: $20,000
D: $40,000
Answer: A
1. Calculate total ratio parts: 3 + 2 + 1 = 6.
2. Determine value per ratio part: $120,000 / 6 = $20,000.
3. Calculate Operations department's total share: 1 part * $20,000 = $20,000.
4. Calculate Marketing department's total share: 2 parts * $20,000 = $40,000.
5. Calculate individual Marketing team leader's share: $40,000 / 5 = $8,000.
6. Find the difference: $20,000 (Operations) - $8,000 (Marketing Team Leader) = $12,000.
Why others are wrong:
A — Correct.
B — This is the amount received by a single Marketing team leader, not the requested difference.
C — This is the total amount received by the Operations department, not the requested difference.
D — This is the total amount received by the Marketing department, not the individual share or the difference.
Discuss About this Question.
A company's annual profit of $120,000 is to be distributed among three partners: X, Y, and Z. The distribution is based on their initial investments, which were in the ratio of 3:5:7, respectively.
What percentage of the total profit does Partner Y receive less than Partner Z?
A: 20%
B: 13.33%
C: 28.57%
D: 40%
Answer: B
1. Calculate the total number of ratio parts: 3 (for X) + 5 (for Y) + 7 (for Z) = 15 parts.
2. Determine the value of one ratio part: Total profit / Total parts = $120,000 / 15 = $8,000 per part.
3. Calculate Partner Y's share: 5 parts * $8,000/part = $40,000.
4. Calculate Partner Z's share: 7 parts * $8,000/part = $56,000.
5. Find the difference between Partner Z's share and Partner Y's share: $56,000 - $40,000 = $16,000.
6. Express this difference as a percentage of the total profit: ($16,000 / $120,000) * 100%.
7. Calculate the percentage: (2/15) * 100% ≈ 13.33%.
Why others are wrong:
A — This represents Partner X's share ($24,000) as a percentage of the total profit ($120,000), which is 24/120 = 20%.
C — This represents the difference between Y and Z's shares ($16,000) as a percentage of Z's share ($56,000), which is 16/56 ≈ 28.57%.
D — This represents the difference between Y and Z's shares ($16,000) as a percentage of Y's share ($40,000), which is 16/40 = 40%.
Discuss About this Question.
Ad Slot (Above Pagination)
Discuss About this Question.