Question

In a mixture, unbroken and broken rice grains are in the ratio 3 : 2. How much fraction of the mixture must be drawn off and substituted with broken grains, so that the ratio of unbroken and broken grains becomes 1 : 1? ​

Answer 1

1/6 is the ratio of rice that must be substituted with broken rice to obtain the final ratio as 1:1

Step-by-step explanation:

Given, initial ratio of unbroken to broken rice in the mixture = 3:2

Let the total amount of rice be x

Thus, initially, the amount of unbroken rice in the mixture will be 3/4x

The amount of broken rice will be 2/4x

The final rice mixture contains the ratio of unbroken and broken rice as 1:1

∴ The amount of unbroken rice in final mixture = 1/2x

The amount of unbroken rice that is removed = ¾ x – ½ x = ¼ x

Thus, ¼ x of the unbroken rice is to be removed

However, the rice mixture contains the ratio of 3:2

So; when ¼ x rice is removes it will contain 2/3x of broken rice

Hence, the mixture = ¼ x + 2/3 x  

        = 1/6 x

Thus, 1/6 x of the mixture must be substituted with broken rice to make the final ratio as 1:1