कुत्तों और मुर्गियों के एक समूह में, पैरों की संख्या सिरों की संख्या के दोगुने से 14 अधिक है। कुत्तों की संख्या ज्ञात कीजिये ?

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

Explanation

The problem can be modeled using a linear equation. Let 'd' be the number of dogs and 'c' be the number of chickens.
Total heads = d + c. Total legs = 4d + 2c.
The given condition is: Total legs = 2 * (Total heads) + 14.
Substituting the expressions gives: 4d + 2c = 2(d + c) + 14.
Simplifying the equation: 4d + 2c = 2d + 2c + 14.
The '2c' term cancels out on both sides, leaving 4d = 2d + 14.

Option B: If there were 6 dogs, the number of legs would be 4(6) = 24. The equation 2d = 14 would become 2(6) = 12, which is not equal to 14. This violates the core condition of the problem.
Option C: If there were 10 dogs, the number of legs would be 4(10) = 40. The equation 2d = 14 would become 2(10) = 20, which is not equal to 14. This contradicts the problem's statement.
Option D: If there were 8 dogs, the number of legs would be 4(8) = 32. The equation 2d = 14 would become 2(8) = 16, which is not equal to 14. This does not satisfy the given relationship.

Visual 1: No visual aid is required for this type of mathematical reasoning question.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving linear equations from word problems as background academic context rather than a clinical decision trigger.
This question tests logical reasoning and problem-solving skills, which are essential for nurses.
Nurses often need to perform calculations for medication dosages, IV drip rates, and other clinical parameters, which requires strong mathematical aptitude.
What if the problem stated the number of legs was 20 more than twice the number of heads? In that case, the equation would be 2d = 20, and the number of dogs would be 10.

How to Approach the Question

First, carefully read the word problem to understand the given information and what needs to be found.
Identify the unknown quantities and assign variables to them (e.g., let 'd' be dogs and 'c' be chickens).
Translate the relationships described in the problem into mathematical equations.
Formulate the primary equation based on the main condition: (Number of legs) = 2 * (Number of heads) + 14.
Substitute the variable expressions for legs and heads into this equation: 4d + 2c = 2(d + c) + 14.
Solve the resulting algebraic equation for the desired variable ('d'). Notice how the variable 'c' cancels out, simplifying the problem.

Concept Tested & Keywords

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Practise the full ESIC Nursing Officer - 2019 (Shift-2)

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