Question

A bottle contains 50 liters of milk. From this bottle 5 liters of milk was taken out and replaced with water. This process was repeated further for three times. How much milk is now contained in the bottle?

• A. 32.8 litres
• B. 34.4 litres
• C. 36.8 litres
• D. 46.5 litres

Hint:

Use the successive dilution formula: milk left = original volume times (1 minus removed fraction) raised to the number of times the process happens, here 4 times.

Answer 1

The Correct Option is A

Step 1: Track the milk after the first removal.
Start with 50 litres of pure milk. Take out 5 litres of milk (the bottle is pure milk at this point) and pour in 5 litres of water. Milk left $= 50 - 5 = 45$ litres out of 50 litres total.

Step 2: Find the fraction of milk left after round 1.
Fraction of milk in the bottle now $= \frac{45}{50} = 0.9$. Every time you take out 5 litres of the mixture, you remove 10 percent of whatever milk is currently in the bottle, since 5 out of 50 is 10 percent. So each round multiplies the milk amount by 0.9.

Step 3: Apply this 0.9 multiplier three more times.
After round 2: $45 \times 0.9 = 40.5$ litres.
After round 3: $40.5 \times 0.9 = 36.45$ litres.
After round 4: $36.45 \times 0.9 = 32.805$ litres.

Step 4: Round the final value.
32.805 litres rounds to 32.8 litres, which matches the direct check of $50 \times 0.9^4$.

Final Answer:
The milk left in the bottle is about 32.8 litres. \[ \boxed{32.8 \text{ litres}} \]