Multiple choice

A factory needs to obtain the right chemical solution which is a mix of sodium nitrate and molten caustic soda to give black finish to steel parts. In a trial process, 'c ' litres of the pure chemical solution was drawn from a furnace tank containing 729 litres of the pure chemical solution and replaced with water. The resulting mixture was thoroughly mixed to obtain a homogeneous aqueous solution and then again 'c' litres of this resulting solution was withdrawn and replaced with water. The resulting mixture was again thoroughly mixed to obtain a homogeneous aqueous solution. This procedure was repeated 6 times till the tank contained 64 litres of the pure chemical solution. Find the value of 'c'.

  1. 81

  2. 162

  3. 243

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Final amount = Initial * (1 - c/729)^n. 64 = 729 * (1 - c/729)^6. (64/729) = (1 - c/729)^6. (2/3)^6 = (1 - c/729)^6. 2/3 = 1 - c/729. c/729 = 1/3. c = 243.

AI explanation

Using the formula for replacement, Final Amount = Initial Amount * (1 - Replacement Volume / Total Volume)^n. Here, 64 = 729 * (1 - c / 729)^6. This simplifies to (64 / 729) = ((729 - c) / 729)^6, meaning (8 / 27)^3 = ((729 - c) / 729)^6. Taking the cube root of both sides gives 8 / 27 = ((729 - c) / 729)^2, so the square root gives 2 / 3 = (729 - c) / 729. Solving for c yields c = 243.

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