West Bengal Board Solutions for Chapter: Mixture, Exercise 2: Let's work out - 12

In a certain type of brass the ratio of measurements of Copper and Zinc is $5:2$. Let's work out what will be the ratio of Copper and Zinc in $28 \mathrm{kg}$ of brass if $4 \mathrm{kg}$ of Copper is added to it. 

In two different kinds of washing powder the ratios of measurement of soda and soap powder are $2:3$ and $4:5$. Let's work out the part of the soap powder in the new washing powder which is prepared by mixing $10 \mathrm{kg}$ of first washing powder with $18 \mathrm{kg}$ of second washing powder. 

$\frac{1}{3}$ and $\frac{1}{4}$ parts two similar vessels contain Fruit juice. I filled water in the remaining empty part of these vessels and poured the juice mixed with water of the two vessels into another big vessel. Let's work out the ratio of measurement of fruit and water in the new vessel. 

Reshmi Khatun has filled $3$ similar glasses of equal size with beverage. The ratios of measurements of water and syrup in these three glasses are $3:1, 5:3$ and $9:7$ respectively. I poured the beverage of these three glasses into a big vessel. Let's work out the ratio of measurements of water and syrup in the new vessel. 

I prepared two types of beverages in my house. The ratio of measurement of syrup and water in two types of beverage are $2:7$ and $1:5$ respectively. Let's try to calculate what ratio of the measurements of the two beverages needs to be mixed so that the ratio of syrup and water will be$5:21$ 

Answer:

Let's think $x \mathrm{litres}$ of the first beverage mixed with $y \mathrm{litre}$ of the second beverage. 

$\therefore$ The quantity of syrup in the $x \mathrm{litre}$ of the  first beverage$=\frac{2}{9}\times x \mathrm{litres}=\frac{2x}{9} \mathrm{litres}$
And the quantity of water is $=\frac{\boxed{?}}{\boxed{?}}\times \boxed{?} \mathrm{litre}=\frac{7\mathrm{x}}{9} \mathrm{litre}$
$\therefore$ The quantity of syrup in the $y \mathrm{litre}s$ of the second beverage is $\frac{1}{6}\times y \mathrm{litres}$ $=\frac{y}{6} \mathrm{litres}$
And the quantity of water is $\frac{5}{6}\times y \mathrm{litres}=\frac{5y}{6} \mathrm{litres}$
$\therefore$The quantity of syrup in the new beverage is $=\frac{2x}{9} \mathrm{litres}+\frac{y}{6} \mathrm{litres}$

$=\left(\frac{2x}{9}+\frac{y}{6}\right) \mathrm{litre}$
And the quantity of water is $=\frac{7x}{9} \mathrm{litres}+\frac{5y}{6} \mathrm{litres}$

$=\left(\frac{7x}{9}+\frac{5y}{6}\right) \mathrm{litres}$

According to the condition, 

$\frac{{\displaystyle \frac{2x}{9}}+{\displaystyle \frac{y}{6}}}{\frac{7x}{9}+\frac{5y}{6}}=\frac{5}{21}$

$\Rightarrow 21\left(\frac{2x}{9}+\frac{y}{6}\right)=5\left(\frac{7x}{9}+\frac{5y}{6}\right)$

$\Rightarrow 21\left(\frac{4x+3y}{18}\right)=5\left(\frac{14x+15y}{18}\right)$

$\Rightarrow 21\left(4x+3y\right)=5\left(14x+15y\right)$

$\Rightarrow 84x+63y=70x+75y$

$\Rightarrow 84x-70x=75y-63y$

$\Rightarrow 14x=12y$

$\Rightarrow \frac{x}{y}=\frac{12}{14}=\frac{6}{7}$

$\therefore x:y=6:7$

Two different types of stainless steel contain Chromium and Steel in the ratio of measurement of $2:11$and $5:21$ respectively. Let's work out in what proportion these two types of steel should be mixed, so that the ratio of measurement of Chromium and Steel becomes $7:32$

The ratio of water and the remaining portion in a syrup is $89:11$. How many litres of water is to be added to the syrup to make the ratio $90:10$.

The ratio of the volumes of three bottles is $5:3:2$. These bottles are filled with the solution of phenyl and water. The ratio of measurement of phenyl and water in three bottles each are $2:3, 1:2$ and $1:3$ respectively. $\frac{1}{3}$ part of the first bottle, $\frac{1}{2}$ part of the second bottle and $\frac{2}{3}$ part of the third bottle are mixed together now. What is the ratio of phenyl and water in the new solution?