Discussion

Question:

From a container full of pure milk, ‘r’ litres of milk was drawn & replaced with water. ‘r’ litres of the solution was again drawn & replaced with water. The ratio of milk & water was then 64 : 225. What fraction of the container’s capacity is ‘r’?

Explanation:

Let the initial quantity of container = V liters.

∴ Initial quantity of milk = V liters [initially only milk is present]
∴ Final quantity of milk = $\frac{64}{64 + 225}$ × V = $\frac{64}{289} V$

Fraction of milk removed = $\frac{r}{V}$
∴ Fraction of milk remaining = $(1 - \frac{r}{V})$
This process is repeated twice.

∴ Final quantity of milk = (Initial quantity of milk) × ${(1 - \frac{r}{V})}^{2}$

⇒ $\frac{64}{289} V$ = $V {(1 - \frac{r}{V})}^{2}$

⇒ $\frac{64}{289}$ = ${(1 - \frac{r}{V})}^{2}$

⇒ $\frac{8}{17}$ = $(1 - \frac{r}{V})$

⇒ $\frac{r}{V}$ = $\frac{9}{17}$

Hence, option (a).

» Your doubt will be displayed only after approval.

Discussion

Doubts

Feedback