8 litres are drawn from a flask containing milk and then filledwith water. The operation is performed 3 more times. Theratio of the quantity of milk left and total solution is 81/625.How much milk the flask initially holds?

Step 1: Understand the problem setup

• Each time, 8 litres of milk is removed and replaced with 8 litres of water.
• This process is done a total of 4 times.
• After 4 operations, the ratio of milk left to the total solution is 81:625.
• We are to find the initial quantity of milk (total volume of flask).

Step 2: Use the formula for repeated replacement

After n operations, the amount of milk left is given by:

Milk left = Total × (1 - x/Total)^n

Where:

• Total = total initial quantity of milk in litres (let it be T)
• x = quantity removed and replaced each time = 8 litres
• n = number of times the operation is done = 4

Step 3: Apply the formula

Milk left / Total = (1 - 8/T)^4 = 81/625

Step 4: Take fourth root of both sides

(1 - 8/T) = (81/625)^(1/4) = (3/5)

Step 5: Solve for T

1 - 8/T = 3/5
=> 8/T = 1 - 3/5 = 2/5
=> T = 8 × 5 / 2 = 40 / 2 = 20 litres

Answer: 20 litres

The flask initially holds 20 litres of milk.