Krishna keeps hens (2 legs) and goats (4 legs). If the total number of heads is 81 and the total number of legs is 234, how many goats does Krishna have?
Aptitude
Linear Equation
Difficulty: Easy
Choose an option
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A45
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B24
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C36
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DCannot be determined
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E30
Answer
Correct Answer: 36
Explanation
Introduction: Another heads-and-legs linear system. Each animal contributes one head, hens have 2 legs, goats have 4 legs. Solve for the number of goats.
Given Data / Assumptions:
- h + g = 81.
- 2h + 4g = 234.
- h, g are nonnegative integers.
Concept / Approach: Simplify the legs equation by dividing by 2, then eliminate h to isolate g.
Step-by-Step Solution:
h + g = 81 … (1)h + 2g = 117 … (2) (after dividing by 2)Subtract (1) from (2): g = 36.Hence h = 45 (sanity check).Verification / Alternative check: Legs: 2*45 + 4*36 = 90 + 144 = 234, checks out.
Why Other Options Are Wrong: Other counts lead to wrong total legs; “Cannot be determined” is incorrect because the system is solvable and unique.
Common Pitfalls: Missing the divide-by-2 simplification, which makes arithmetic cleaner.
Final Answer: 36