1964 AHSME Problems/Problem 14

Problem

A farmer bought $749$ sheep. He sold $700$ of them for the price paid for the $749$ sheep. The remaining $49$ sheep were sold at the same price per head as the other $700$ . Based on the cost, the percent gain on the entire transaction is:

$\textbf{(A)}\ 6.5 \qquad \textbf{(B)}\ 6.75 \qquad \textbf{(C)}\ 7 \qquad \textbf{(D)}\ 7.5 \qquad \textbf{(E)}\ 8$

Solution

Let us say each sheep cost $x$ dollars. The farmer paid $749x$ for the sheep. He sold $700$ of them for $749x$ , so each sheep sold for $\frac{749}{700} = 1.07x$ .

Since every sheep sold for the same price per head, and since every sheep cost $x$ and sold for $1.07x$ , there is an increase of $\frac{1.07x - 1x}{1x} = 0.07$ , or $7\%$ , which is option $\boxed{\textbf{(C}}$

1964 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
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1964 AHSME Problems/Problem 14

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