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.