Question

A barrel contains 60 liters of wine. Four liters of wine is taken out and replaced by soda. This process is repeated two more times. How much wine (in litres) is now contained by the container?
1. 52.16
2. 49
3. 46
4. 43

Answer 1

Correct Answer - Option 2 : 49

Given:

Capacity of barrel = 60 liters.

4 liters of wine is taken out and replaced by soda and 

this process is repeated two more times. (a total of 3 times)

Formula used:

x(1 - y/x)ⁿ = x(1 - y/x)ⁿ

where n = number of replacements.

Calculation:

Suppose a solution contains x units of wine

from which y units are taken out and replaced by soda

After n repeated operations, quantity of pure wine

remaining in solution:

⇒ x(1 - y/x)n = x(1 - y/x)n

So, wine in the barrel now:

⇒ 60(1 - 4/60)³ = 60(1 - 1/15)³

⇒ 48.78 ≈  49