A, B, and C spend 80%, 85%, and 75% of their salaries respectively. The total of their salaries is ₹1,08,000. If their savings are in the ratio 8 : 9 : 20, what is the difference between the salaries of A and C?

1. A

   25,600

2. B

   18,000

3. C

   25,800

4. D

   24,000

Appeared in: JSSH Staff Nurse - 2019

Explanation

• The correct option is derived by first calculating each person's savings percentage (A: 20%, B: 15%, C: 25%).
• Using the formula Salary = Savings / Savings Percentage and the given savings ratio (8:9:20), the salary ratio is found to be 40:60:80, which simplifies to 2:3:4.
• The total salary of ₹1,08,000 is divided according to this ratio. The sum of ratio parts is 2+3+4=9.
• The value of one ratio part is ₹1,08,000 / 9 = ₹12,000.
• The difference in salary between A (2 parts) and C (4 parts) is 2 parts.
• Therefore, the difference is 2 × ₹12,000 = ₹24,000.

Why Other Options Were Wrong

• Option A: This value is incorrect. It may result from a calculation error, such as miscalculating the value of one ratio part or the salary ratio itself.
• Option B: This value (₹18,000) might be obtained if the difference in ratio parts was incorrectly calculated as 1.5 (e.g., 3 - 1.5) instead of 2.
• Option C: This is a random incorrect value likely resulting from a simple arithmetic mistake during one of the calculation steps.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the understanding of percentages, ratios, and proportions, and their application in problems related to income, expenditure, and savings as background academic context rather than a clinical decision trigger.
• This is a quantitative aptitude question designed to test mathematical reasoning and problem-solving skills.
• While not directly related to clinical practice, these skills are essential for nurses for tasks like medication dosage calculations, interpreting data from charts, and managing resources.
• What if the savings ratio was 4:3:5? The salary ratio would be (4/0.2) : (3/0.15) : (5/0.25) = 20:20:20 or 1:1:1. Each person's salary would be ₹1,08,000 / 3 = ₹36,000, and the difference between A and C's salary would be zero.

How to Approach the Question

• First, carefully read the question to identify all the given information: expenditure percentages for A, B, and C; their total salary; and the ratio of their savings.
• Determine the goal of the question, which is to find the difference between the salaries of A and C.
• Establish the relationship between expenditure, savings, and salary. Remember that Savings % = 100% - Expenditure %.
• Use the savings ratio and the calculated savings percentages to find the ratio of the salaries. The key formula is Salary is proportional to (Savings Ratio Part / Savings Percentage).
• Once you have the salary ratio, sum its parts. Divide the total salary by this sum to find the value of one part of the ratio.
• Finally, calculate the difference in the ratio parts for A and C and multiply it by the value of one part to get the final answer.

Concept Tested & Keywords

• Concept Tested: This question tests the understanding of percentages, ratios, and proportions, and their application in problems related to income, expenditure, and savings.
• Stem keywords: spend, salaries, savings, ratio, total salary
• Lead-in keywords: what is the difference

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Qd_TVF61L8RdexW8d48yoq

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