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?
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?
The correct option is A 1: 5
Let1: 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 at 5 cents per ounce ) + (k ounces at 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).
He earned 20% profit doing this, 7(1+k) must be 20% more than 5+6k.
Hence, we have the equation 7+7k = 6 + 365 k
⇒ k = 5
Therefore, the required ratio is 1: k = 1: 5
1: 5
Let1: 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 at 5 cents per ounce ) + (k ounces at 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).
He earned 20% profit doing this, 7(1+k) must be 20% more than 5+6k.
Hence, we have the equation 7+7k = 6 + 365 k
⇒ k = 5
Therefore, the required ratio is 1: k = 1: 5
