Question

In a chemical experiment two NaOH solution bottles are used Bottle A contains salt and water in the ratio 7 : 3 and bottle B contains salt and water in the ratio 4 : 3. In what proportion should the quantities be taken from A and B to give the 2 : 1 NaOH solution?

• A. $2:1$
• B. $10:7$
• C. $20:7$
• D. $1:2$

Answer 1

The correct option is C $20:7$

From the given data,

bottle A contains NaOH : water=7 : 3.

Let us take an amount x from A for our purpose.

Then the amount of NaOH=$x\times \frac{7}{7+3}=\frac{7x}{10}$ and

the amount of water= $x\times \frac{3}{7+3}=\frac{3x}{10}$.

Again bottle B contains NaOH : water=4 : 3.

Let us take an amount y from B for our purpose.

Then the amount of NaOH=$y\times \frac{4}{4+3}=\frac{4y}{7}$ and

the amount of water= $y\times \frac{3}{4+3}=\frac{3y}{7}$.

So, after mixing, the amount of NaOH=$\frac{7x}{10}+\frac{4y}{7}=\frac{49x+40y}{70}$ and

the amount of water=$\frac{3x}{10}+\frac{3y}{7}=\frac{21x+30y}{70}$.

$\therefore$ By the given condition,

$\frac{49x+40y}{70}:\frac{21x+30y}{70}=2:1⟹49x+40y=42x+60y⟹7x=20y⟹x:y=20:7.$

So the required ratio is 20 : 7.

Ans- Option C.