Question

In mixture A, the ratio of coco and sugar is 3:2 and in mixture B, the ratio of coffee and sugar is 7 : 3. These two were mixed together in the ratio 2:3 to make mixture C. Now equal quantities of C and milk are mixed. Find the percentage of sugar in the mixture.

Answer 1

Let's denote the quantities of cocoa and sugar in mixture A as 3 x and 2 x respectively, and in mixture B as 7 y and 3 y respectively.

The ratio of cocoa to sugar in mixture A is 3:2, so we can express the quantities of cocoa and sugar in A as 3 x and 2 x respectively.

Similarly, the ratio of coffee to sugar in mixture B is 7:3, so we can express the quantities of coffee and sugar in B as 7 y and 3 y respectively.

Now, the two mixtures A and B are mixed together in the ratio 2:3 to form mixture C. Therefore, the quantities of cocoa and sugar in mixture C are 2(3 x)+3(7 y)=6 x +21 y and 2(2 x)+3(3 y)=4 x +9 y respectively.

Now, equal quantities of mixture C and milk are mixed. Let z be the common factor for the amounts of sugar in mixture C and milk.

The total quantity of sugar in the final mixture is 4 x +9 y +z , and the total quantity of the mixture is 6 x +21 y +2 z.

The percentage of sugar in the mixture is given by the formula: Percentage of Sugar=$\frac{4x+9x}{6x+21y+2x}$×100

Percentage of Sugar=$\frac{4x+9x}{6x+21y+2x}$×100

If the given answer is 17%, then we can set up the equation: $\frac{4x+9x}{6x+21y+2x}$×100=17

Hence, the percentage of sugar in the mixture is 17%.