From a container having pure milk, 40% is replaced by water and the process is repeated thrice. At the end of the third operation, the purity of milk is:

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 26 Jun, 2024 Shift 1)

Answer 1

Given:

Initial purity of milk = 1 (pure milk)

Percentage of milk replaced by water each time = 40% = 0.40

Number of operations = 3

Formula Used:

Remaining purity of milk after each operation = Initial purity × (1 - Replacement percentage)^{Number of operations}

Calculation:

Initial purity of milk = 1

Replacement percentage = 0.40

Number of operations = 3

Remaining purity after 3 operations:

⇒ 1 × (1 - 0.40)³

⇒ 1 × (0.60)³

⇒ (0.60)³

⇒ 0.60 × 0.60 × 0.60

⇒ 0.216

The purity of milk at the end of the third operation is 0.216.

Alternate Method

Total : Remaining

100 : 60 (100 - 40)

100 : 60

------------------------------

125 : 27

Purity of Milk = [27/125] × 100 = 21.6%

So, the correct answer is Option 4.

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