In a bag, there are coins of 25 paise, 50 paise and Re 1 in the ratio of 4:2:1. In there is Rs. 15 in total, how many 50 paise coins are there?

Appeared in: DSSSB - 28 August 2019 (Shift-1)

Explanation

The ratio of coins (25p, 50p, Re 1) is 4:2:1. Let the number of coins be 4x, 2x, and x respectively.
The total value of the coins is Rs. 15. The equation representing the total value is (4x × 0.25) + (2x × 0.50) + (x × 1.00) = 15.
Simplifying the equation gives 1x + 1x + x = 15, which results in 3x = 15. Solving for x gives x = 5.
The number of 50 paise coins is given by the expression 2x. Substituting x = 5, we get 2 × 5 = 10 coins.

Option A: This is incorrect. If there were 16 coins of 50 paise, then 2x = 16, meaning x = 8. This would lead to a total value of (4×8×0.25) + (16×0.50) + (1×8×1.00) = 8 + 8 + 8 = Rs. 24, which contradicts the given total of Rs. 15.
Option C: This is incorrect. If there were 8 coins of 50 paise, then 2x = 8, meaning x = 4. This would lead to a total value of (4×4×0.25) + (8×0.50) + (1×4×1.00) = 4 + 4 + 4 = Rs. 12, which is not the given total of Rs. 15.
Option D: This is the number of 25 paise coins, not 50 paise coins. Using x=5, the number of 25 paise coins is 4x = 4 × 5 = 20.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving ratio and proportion problems involving currency as background academic context rather than a clinical decision trigger.
This type of ratio problem is a fundamental concept in quantitative aptitude tests, which are common in various competitive examinations, including those for nursing positions.
The core skill demonstrated is translating a word problem into a mathematical equation and solving it systematically.
This problem-solving skill is transferable to clinical settings, such as calculating medication dosages based on weight ratios or diluting solutions.

How to Approach the Question

First, carefully read the problem to identify the given information: the types of coins, the ratio of their quantities, and the total monetary value.
Represent the unknown number of each coin type using a single variable (e.g., 'x') multiplied by its corresponding ratio number (4x, 2x, x).
Formulate a linear equation by summing the monetary values of each group of coins. Ensure all values are in the same unit (either all in Rupees or all in paise). The equation is: (4x × 0.25) + (2x × 0.50) + (x × 1.00) = 15.
Solve the equation for the variable 'x'.
Use the value of 'x' to calculate the specific quantity the question asks for, which is the number of 50 paise coins (2x).
As a final check, you can calculate the number of all coin types and verify that their total value equals the given amount (Rs. 15).

Concept Tested & Keywords

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Practise the full DSSSB - 28 August 2019 (Shift-1)

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