Ratios & Proportion

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Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce, making a profit of 20 percent. What was the ratio of the mixture?









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Option(B) is correct

Let $1:k$ be the ratio in which Joseph mixed the two types of rice.

 Then a sample of $(1+k)$ ounces of the mixture should equal 1 ounce of rice of the first type, and $k$ ounces of rice of the second type.

The rice of the first type costs 5 cents an ounce and that of the second type costs 6 cents an ounce. Hence, it cost him:

(1 ounce  5 cents per ounce) + (k ounces  6 cents per ounce) = $5 + 6k$

Since he sold the mixture at 7 cents per ounce, he must have sold the net $1+k$ ounces of the mixture at $7(1+k)$.

Since he earned $20\%$ profit doing this, $7(1+k)$ must  be  $20\%$  more  than $5+6k$.

Hence, we have the equation

\(\begin{align*} 7(1+k)&=\left(1+\dfrac{20}{100}\right)(5+6k)\\ 7+7k&=\left(\dfrac{120}{100}\right)(5+6k)\\ 7+7k&=\dfrac{6}{5}(5+6k)\\ 7+7k&=6+\dfrac{36k}{5}\\ 1&=\dfrac{k}{5}\\ k&=5 \end{align*}\)

Hence, the required ratio is $1:k$= 1 : 5

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