The total amount invested by three persons A, B and C is Rs 1,290, in which A's share is 3/2 times that of B and B's share is 7/4 times that of C. Then C's share is:

1. A

   Rs. 320

2. B

   Rs. 630

3. C

   Rs. 520

4. D

   Rs. 240

Appeared in: ESIC Nursing Officer - 2019 (Shift-2)

Explanation

• The solution requires expressing the shares of A and B as multiples of C's share (let's call it 'x').
• B's share is (7/4)x, and A's share becomes (3/2) * (7/4)x = (21/8)x.
• An equation is formed by summing the shares: (21/8)x + (7/4)x + x = 1290.
• Solving this linear equation for x gives the value of C's share.
• The calculation (21x + 14x + 8x) = 10320 leads to 43x = 10320, which results in x = 240.

Why Other Options Were Wrong

• Option A: This is an incorrect value derived from a calculation error. If C's share were Rs. 320, the total investment would not be Rs. 1,290.
• Option B: This value represents A's share, not C's. After finding C's share (Rs. 240), B's share is (7/4)*240 = Rs. 420, and A's share is (3/2)*420 = Rs. 630.
• Option C: This is an incorrect value resulting from a miscalculation. It does not fit the ratios provided in the question.

Related Visual

• Visual 1: Flowchart: A flowchart can illustrate the step-by-step process: 1. Define C's share as 'x'. 2. Express A's and B's shares in terms of 'x'. 3. Form the equation A + B + C = 1290. 4. Solve the equation for 'x' to find C's share. 5. Verify the total.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving problems involving ratio and proportion as background academic context rather than a clinical decision trigger.
• This question tests foundational quantitative aptitude, specifically in ratio and proportion.
• While not a clinical question, these problem-solving skills are essential for interpreting data and performing calculations in various fields.
• What if the question asked for the difference between A's and C's share? You would first calculate both shares (A=630, C=240) and then find the difference: 630 - 240 = Rs. 390.

How to Approach the Question

• First, carefully read the problem to understand the relationships between the shares of A, B, and C.
• Identify the base person whose share can be used to define the others. Here, C is the best choice as B is defined by C, and A is defined by B.
• Assign a variable (e.g., 'x') to the base share (C's share).
• Write down the expressions for the other shares (A and B) in terms of 'x'.
• Set up an equation by summing all the shares, which equals the total investment given (Rs. 1,290).
• Solve the algebraic equation for 'x'. The value of 'x' will be the answer, as the question asks for C's share.

Concept Tested & Keywords

• Concept Tested: Solving problems involving ratio and proportion
• Stem keywords: total amount invested, share, A's share, B's share, C's share
• Lead-in keywords: Then C's share is

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