# In a mixture, the ratio of milk and water is in the ratio 5 : 3. If 40 liters of mixture is extracted and 10 liters of water is added to the remaining

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In a mixture, the ratio of milk and water is in the ratio 5 : 3. If 40 liters of mixture is extracted and 10 liters of water is added to the remaining mixture then the ratio of milk and water becomes 5 : 4. Find the original quantity of mixture.

1. 135 liters
2. 130 liters
3. 120 liters
4. 115 liters
5. None of these

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Correct Answer - Option 3 : 120 liters

Given:

Initial ratio of milk and water in the mixture = 5 : 3

The supposed ratio of milk and water in the mixture = 5 : 4

Quantity of extracted mixture = 40 liters

Quantity of water added = 10 liters

Concept used:

Supposed ratio = (Initial quantity of milk – The extracted quantity of milk)/(Initial quantity of water – The extracted quantity of water + Quantity of water added)

Calculation:

Let the quantity of milk and water in the initial mixture is 5x and 3x respectively.

Then, [5x – {40 × (5/8)}]/[3x – {40 × (3/8)} + 10] = 5/4

⇒ [5x – 25]/[3x – 15 + 10] = 5/4

⇒ 20x – 100 = 15x – 25

⇒ 5x = 75

⇒ x = 15

Original quantity of milk = 5 × 15

⇒ 75 liters

Original quantity of water = 3 × 15

⇒ 45 liters

Then, Original quantity of mixture = 75 + 45

⇒ 120 liters

∴ The original quantity of mixture is 120 liters.