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:kbe 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 7+7k=6+365k
⇒k=5
Hence, the required ratio is 1 : k=1 : 5
1:5
Let1:kbe 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 7+7k=6+365k
⇒k=5
Hence, the required ratio is 1 : k=1 : 5
