Multiple choice

A thief has stolen 16L of beer from a container and replaced with the same quantity of water. He again repeated this process 2 times more. Thus, the ratio of the beer to the total quantity in the container becomes 125:216. Find the initial quantity of beer in the container?

  1. (a) 108L

  2. (b) 72L

  3. (c) 80L

  4. (d) 96L

  5. (e) 84L
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The formula for replacement is: Final quantity of beer / Initial quantity = (1 - x/V)^n. Here, 125/216 = (1 - 16/V)^3. Taking the cube root, 5/6 = 1 - 16/V. Thus, 16/V = 1/6, so V = 96L.

AI explanation

Let the initial quantity of beer be x litres, and after replacing 16 litres three times the remaining beer ratio to the total quantity is (1 minus 16/x) cubed equals 125/216. Taking the cube root of both sides gives 1 minus 16/x = 5/6, so 16/x = 1/6. Solving this equation gives x = 96 litres as the initial quantity of beer in the container.

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