Question

A tin container contains 50 litres of cow milk. From this container 5 litres cow milk was taken out and replaced with soya milk. This process was repeated further two more times. How much cow milk is there in the container now?

• A. 364.5 litres
• B. 36.45 litres
• C. 3.645 litres
• D. 40 litres

Hint:

Cow milk left = \(50(1 - 5/50)^3\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Each time we take out 5 litres of the mixture and add soya milk, the cow milk left is multiplied by the same fraction.

Step 2: Find the fraction kept.
Total volume stays 50 litres. Removing 5 litres removes \(\frac{5}{50} = \frac{1}{10}\) of the cow milk. So \(\frac{9}{10}\) of the cow milk stays after each step.

Step 3: Apply three times.
The process is done once and then repeated two more times, so 3 times in all. \[ 50 \times \left(\frac{9}{10}\right)^3 = 50 \times \frac{729}{1000} = 36.45 \]

Step 4: Check the options.
364.5 is more than 50, which is impossible. 3.645 has the decimal point in the wrong place. 40 would be the amount left if only one replacement of 10 litres was done, which does not match this process.

Final Answer:
The cow milk left is 36.45 litres. \[ \boxed{36.45 \text{ litres}} \]