Question

In a farmhouse, there are only horses and sheep. If 50% of the horses were sheep, then there would have been 50% more sheep than the number of horses. What percentage of all the animals are horses?

• A. 60%
• B. 40%
• C. 50%
• D. 80%

Hint:

Express all variables in terms of one variable (e.g., \(S = 0.25H\)) to easily find ratios and percentages.

Answer 1

The Correct Option is D

Step 1: Set up the Equations:
Let \(H\) be horses and \(S\) be sheep. New scenario: 50% of horses become sheep. New Horses \(H' = 0.5H\). New Sheep \(S' = S + 0.5H\). Step 2: Apply the Condition:
Condition: \(S' = H' + 50% \text{ of } H' = 1.5 H'\). Substitute values: \(S + 0.5H = 1.5(0.5H) = 0.75H\). \(S = 0.75H - 0.5H = 0.25H\). Step 3: Calculate Percentage:
Total animals = \(H + S = H + 0.25H = 1.25H\). Percentage of horses = \(\frac{H}{1.25H} \times 100\). \(% = \frac{100}{1.25} = 80%\).