Given:
Milk to water ratio in the first cup = 7:5.
Milk to water ratio in the second cup = 9:4.
Milk to water ratio in the third cup = 2:9.
Quantity taken from the first cup = 24 liters.
Quantity taken from the second cup = 26 liters.
Required milk to water ratio in the final mixture = 1:1.
Formula Used:
Milk in mixture = (Milk ratio / Total ratio) × Total quantity.
Water in mixture = (Water ratio / Total ratio) × Total quantity.
Final ratio condition: Milk = Water.
Calculation:
For the first cup:
Total ratio = 7 + 5 = 12
Milk in 24 liters = (7/12) × 24 = 14 liters
Water in 24 liters = (5/12) × 24 = 10 liters
For the second cup:
Total ratio = 9 + 4 = 13
Milk in 26 liters = (9/13) × 26 = 18 liters
Water in 26 liters = (4/13) × 26 = 8 liters
Let the quantity taken from the third cup be x liters.
Total ratio = 2 + 9 = 11
Milk in x liters = (2/11) × x = (2x/11)
Water in x liters = (9/11) × x = (9x/11)
Final mixture condition: Milk = Water
14 + 18 + (2x/11) = 10 + 8 + (9x/11)
⇒ 32 + (2x/11) = 18 + (9x/11)
⇒ 32 - 18 = (9x/11) - (2x/11)
⇒ 14 = 7x/11
⇒ x = (14 × 11) / 7
⇒ x = 22
Final Answer:
22 liters of the third cup is to be taken.