A person wants to make a sum of Rs. 16 with 40 coins using 50 paise coins and 25 paise coins. How many coins are there of 25 paise?

Appeared in: KPSC Staff Nurse - 2018

Explanation

The problem can be modeled using two linear equations: one for the total number of coins and one for their total value in paise.
Let 'x' be the number of 50 paise coins and 'y' be the number of 25 paise coins. The two resulting equations are: x + y = 40 (for the count) and 50x + 25y = 1600 (for the value).
Solving these simultaneous equations, for instance by substituting x = 40 - y into the second equation, isolates the variable 'y'.
The calculation 50(40 - y) + 25y = 1600 simplifies to 2000 - 25y = 1600, which gives 25y = 400.
Solving for y (y = 400 / 25) gives the result y = 16. Therefore, there are 16 coins of 25 paise.

Option A: If there are 20 coins of 25 paise (value 500 paise), the remaining 20 coins must be 50 paise (value 1000 paise). The total value is 1500 paise (Rs. 15), which is not the required Rs. 16.
Option B: If there are 24 coins of 25 paise (value 600 paise), the remaining 16 coins must be 50 paise (value 800 paise). The total value is 1400 paise (Rs. 14), not Rs. 16.
Option D: If there are 22 coins of 25 paise (value 550 paise), the remaining 18 coins must be 50 paise (value 900 paise). The total value is 1450 paise (Rs. 14.50), not Rs. 16.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a system of linear equations from a word problem as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude and problem-solving skills, which are essential for many competitive examinations, including those for nursing roles.
The ability to translate word problems into mathematical equations is a fundamental analytical skill applicable in various fields.
What if the total sum was Rs. 15? In that scenario, the number of 25 paise coins would be 20, and the number of 50 paise coins would also be 20.

How to Approach the Question

First, carefully read the question to identify all the given information: the total number of coins (40) and the total value (Rs. 16).
Convert all monetary values to the smallest unit to avoid decimals. Here, convert Rs. 16 to 1600 paise.
Define variables for the unknown quantities. For example, let 'y' be the number of 25 paise coins and 'x' be the number of 50 paise coins.
Formulate two linear equations based on the information. The first equation will represent the total count of coins (x + y = 40). The second will represent the total value (50x + 25y = 1600).
Solve this system of two equations. A common method is substitution: solve one equation for one variable (e.g., x = 40 - y) and substitute that expression into the other equation.
Solve the resulting single-variable equation to find the answer. Then, check your answer by plugging the values back into the original problem statement.

Concept Tested & Keywords

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