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+2 votes

Let $A$ and $B$ be two containers. Container $A$ contains $50$ litres of liquid $X$ and container $B$ contains $100$ litres of liquid $Y$. Liquids $X$ and $Y$ are soluble in each other.

We now take $30$ ml of liquid $X$ from container $A$ and put it into container $B$. The mixture in container $B$ is then thoroughly mixed and $20$ ml of the resulting mixture is put back into container $A$.At the end of this process let $V_{AY}$ be the volume of liquid $Y$ and $V_{BX}$ be the volume of liquid $X$ in container $B$. Which of the following must be TRUE ?

- $V_{AY} < V_{BX}$
- $V_{AY} > V_{BX}$
- $V_{AY} = V_{BX}$
- $V_{AY} + V_{BX}=30$
- $V_{AY} + V_{BX}=20$

+3 votes

Best answer

Volume of liquid $X$ in container $A = 50\,l$, Volume of liquid $Y$ in container $B = 100\,l$

$\rightarrow$ After mixing $30\,ml$ of liquid from $A$ to $B$

In Container $A$ :

- Volume of liquid $X=50l -30\,ml=49970\;ml$

In Container $B$ :

- Volume of liquid $X$ = $30\,ml$ , Volume of liquid $Y$ = $100\,l$
- $\%$ of liquid $X$ = $\frac{30}{100030}$, $\%$ of liquid $Y = \frac{100000}{100030}$

$\rightarrow$ After mixing $20\,ml$ of liquid from container $B$ to $A$:

In Container $A$ :

- Volume of $Y\,(V_{AY})$ = $20*\frac{100000}{100030}=\frac{2000000}{100030}$

In Container $B$ :

- Volume of $X\,(V_{BX})$ = $30-\left(\frac{30}{100030}*20\right) = \frac{3000300}{100030}$

So, $V_{AY} < V_{BX}$, option $(A)$ should be correct.

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