Question

A vessel is full of milk , 15 L of milk is taken out and replaced by water. This process if repeated once more, find the vessel if at the end the ratio of milk to water become 25: 16?​

Answer 1

Given :-

• Vessel is Full of Milk.
• 15 litre milk is removed and replaced by water
• This process is repeated one more Time.
• Ratio of Milk : water now = 25 : 16 .

To Find :-

• initial Capacity of water ?

Formula used :-

• Final concentration = initial concentration( 1 - x/v)^T where x is Removing Quantity and V is Total volume and T is Number of Time .

Solution :-

→ Final concentration of water = (16/25)

→ initial concentration = 1 (Total = Full).

→ Removed Quantity = 15 litre = x

→ Total Volume = Let V .

→ Number of Time = 2

Putting All Values we get :-

→ (16/25) = (1 - 15/V)²

→ (4/4)5)² = (1 - 15/V)²

→ (4/5) = (1 - 15/V)

→ (15/V) = 1 - (4/5)

→ (15/V) = (1/5)

→ V = 15*5

→ V = 75 Litre.

Hence, Initially, Their was 75 Litre of Milk In The vessel when it was Full.

Answer 2

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Given-

vessel full of milk,15 litres of milk is replaced by water and the process is repeated once more

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To find -

initial capacity of water

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Solution-

Final concentration of water be = 16/25

Initial concentration be = 1

Removed quantity = 15 litres or let it be X

Total volume = v

Process = 2 times

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Calculating-

Put the values together-

➠ (16/25) = ( 1 - 15/ V )²

➠ (4/4)×5² = ( 1 - 15/V)²

➠ (4/5) = 1 - (4/5)

➠ (15/V) = (1/5)

➠ V = 15 × 5

➠ V = 75

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${\fbox{\red{Volume~=~75}}}$