A sum of money is to be distributed among A, B, C and D in the ratio of 2:5:4:8. If C gets Rs. 400 more than A, then how much does D receive?

Appeared in: DSSSB -28 August 2019 (Shift-2)

Explanation

The shares of A, B, C, and D are represented as 2x, 5x, 4x, and 8x, respectively, based on the given ratio of 2:5:4:8.
The condition 'C gets Rs. 400 more than A' is translated into the algebraic equation: 4x = 2x + 400.
Solving this equation yields 2x = 400, which means the value of the common multiplier 'x' is 200.
D's share is represented by 8x. Substituting the value of x, D's share is calculated as 8 * 200 = Rs. 1600.

Option B: This value (Rs. 1200) would correspond to a share of 6x (6 * 200). This is an incorrect calculation as D's ratio part is 8, not 6.
Option C: This value (Rs. 400) represents the difference between C's and A's shares (4x - 2x = 2x), and also happens to be A's share (2x). It is not D's share (8x).
Option D: This value (Rs. 1000) corresponds to B's share (5x = 5 * 200). The question asks for D's share.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving problems based on ratios and proportions as background academic context rather than a clinical decision trigger.
Proficiency in ratio and proportion is a fundamental competency for nurses, essential for accurate medication dosage calculations to ensure patient safety.
This mathematical skill is applied when reconstituting powdered drugs, titrating intravenous infusions, and calculating pediatric doses based on body weight.
What if? If a drug vial contained 500 mg in 2 mL, and the prescribed dose was 125 mg, the nurse would use a ratio (500mg/2mL = 125mg/x mL) to find that 0.5 mL is the correct volume to administer.

How to Approach the Question

First, identify the given ratio (2:5:4:8) and the entities it applies to (A, B, C, D).
Represent the share of each entity using a common variable, 'x' (e.g., A's share = 2x, C's share = 4x).
Translate the verbal condition provided in the problem ('C gets Rs. 400 more than A') into a mathematical equation (4x = 2x + 400).
Solve this linear equation to determine the numerical value of 'x'.
Finally, use the value of 'x' to calculate the specific quantity asked in the question, which is D's share (8x).

Concept Tested & Keywords

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Practise the full DSSSB -28 August 2019 (Shift-2)

Attempt every question from this paper in a timed mock, then review the full solution for each one.