An amount of ₹7200 is to be divided among A, B, and C in the ratio 2:3:x. If B gets ₹600 more than A, what is the value of x?

Appeared in: NCL (Northern Coalfields Limited)-NO

Explanation

The problem involves dividing an amount based on a given ratio and an additional condition.
Let the shares of A, B, and C be 2k, 3k, and xk. The condition 'B gets ₹600 more than A' translates to the equation 3k - 2k = 600, which gives k = 600.
The total amount is the sum of the shares: 2k + 3k + xk = 7200.
Substituting k = 600 into the total amount equation: 2(600) + 3(600) + x(600) = 7200.
Simplifying the equation: 1200 + 1800 + 600x = 7200, which leads to 3000 + 600x = 7200.
Solving for x: 600x = 4200, so x = 4200 / 600 = 7.

Option A: If x were 6, the total parts in the ratio would be 2+3+6 = 11. The value of one part would be 7200/11, which is not a whole number and would not result in a difference of exactly ₹600 between B and A's shares based on the initial ratio.
Option B: If x were 4, the total parts would be 2+3+4 = 9. The value of one part would be 7200/9 = ₹800. The difference between B's and A's share would be (3-2) * 800 = ₹800, not ₹600.
Option C: If x were 5, the total parts would be 2+3+5 = 10. The value of one part would be 7200/10 = ₹720. The difference between B's and A's share would be (3-2) * 720 = ₹720, not ₹600.

Visual 1: Infographic: A pie chart showing the division of ₹7200 into three parts labeled A, B, and C, with their respective shares (₹1200, ₹1800, ₹4200) and ratio parts (2, 3, 7).

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Ratio and Proportion as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude, a skill necessary for various calculations in nursing, such as medication dosage, IV drip rates, and interpreting patient data.
While not a direct clinical scenario, the logical reasoning and problem-solving skills are transferable to clinical practice.
What if the problem stated that C gets ₹2400 more than A? The equation would be xk - 2k = 2400. With k=600, this becomes 600x - 1200 = 2400, leading to 600x = 3600, and x = 6.

How to Approach the Question

First, identify all the given information: the total amount, the ratio between the parts (A:B:C as 2:3:x), and the relationship between two of the parts (B's share = A's share + 600).
Represent the shares using a common variable. Let the shares be 2k, 3k, and xk.
Use the relationship between the shares of A and B to form an equation and solve for the common variable 'k'. (3k - 2k = 600).
Once 'k' is found, use the fact that the sum of all shares equals the total amount to form a second equation. (2k + 3k + xk = 7200).
Substitute the value of 'k' into this second equation and solve for the unknown 'x'.

Concept Tested & Keywords

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