An amount of ₹903 is divided among three persons in the ratio of 6 : 2 : 7. The difference (in ₹) between the largest and the smallest shares in the distribution is:

1. A

   341

2. B

   301

3. C

   249

4. D

   367

Appeared in: DSSSB 14 August 2024

Explanation

• The total amount to be divided is ₹903, and the ratio is 6:2:7. The sum of the ratio parts is 6 + 2 + 7 = 15.
• The value of one part is found by dividing the total amount by the sum of the parts: ₹903 ÷ 15 = ₹60.2.
• The largest share corresponds to 7 parts (7 × ₹60.2 = ₹421.4) and the smallest share corresponds to 2 parts (2 × ₹60.2 = ₹120.4).
• The difference between the largest and smallest shares is ₹421.4 - ₹120.4 = ₹301.
• Alternatively, the difference in ratio parts (7 - 2 = 5) multiplied by the value of one part (5 × ₹60.2) also gives ₹301.

Why Other Options Were Wrong

• Option A: This value is incorrect. It may result from an arithmetic error, such as miscalculating the value of one part or the difference between the shares.
• Option C: This is an incorrect value. It could arise from calculation errors, such as miscalculating the value of one part or using the wrong ratio parts for the difference.
• Option D: This value is incorrect. It does not align with the correct calculation. It may be the result of an arithmetic error during multiplication or division.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Division of an amount based on a given ratio as background academic context rather than a clinical decision trigger.
• While this is a mathematics question, strong calculation skills are fundamental in nursing for patient safety.
• Nurses use ratios daily for tasks like medication dosage calculations, titrating IV drips, and mixing cleaning or disinfecting solutions (e.g., a 1:10 bleach solution).
• An error in calculation, similar to miscalculating a share in this problem, could lead to a medication error with serious patient harm.

How to Approach the Question

• First, read the question carefully to identify the key information: the total amount (₹903) and the ratio of division (6:2:7).
• Calculate the sum of the ratio's parts to determine the total number of shares the amount is divided into (6 + 2 + 7 = 15).
• Determine the value of a single share by dividing the total amount by the sum of the parts (₹903 ÷ 15).
• Identify the largest (7) and smallest (2) parts of the ratio as requested by the question.
• Calculate the difference between these parts (7 - 2 = 5).
• Finally, multiply this difference in parts by the value of a single share to find the final answer in rupees.

Concept Tested & Keywords

• Concept Tested: Division of an amount based on a given ratio.
• Stem keywords: amount, ₹903, divided, ratio, 6 : 2 : 7
• Lead-in keywords: difference, largest and the smallest shares

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