Question 29

# There are two drums, each containing a mixture of paints A and B. In drum 1, A and B are in the ratio 18 : 7. The mixtures from drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7. In drum 2, then A and B were in the ratio

Solution

It is given that in drum 1, A and B are in the ratio 18 : 7.

Let us assume that in drum 2, A and B are in the ratio x : 1.

It is given that drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7.

By equating concentration of A

$$\Rightarrow$$ $$\dfrac{3*\dfrac{18}{18+7}+4*\dfrac{x}{x+1}}{3+4} = \dfrac{13}{13+7}$$

$$\Rightarrow$$ $$\dfrac{54}{25}+\dfrac{4x}{x+1} = \dfrac{91}{20}$$

$$\Rightarrow$$ $$\dfrac{4x}{x+1} = \dfrac{239}{100}$$

$$\Rightarrow$$ $$x = \dfrac{239}{161}$$

Therefore, we can say that in drum 2, A and B are in the ratio $$\dfrac{239}{161}$$ : 1 or 239 : 161.