A tank has a mixture of solutions A, B, and C in the ratio 6:9:5. 30 litres of this mixture is drained out, and then 12 litres of solution A and 8 litres of solution C are added to the tank. If the resultant quantity of solution A is 18 litres less than the resultant quantity of solution B, what was the initial quantity of the mixture in the tank (in litres)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 230.
Let the initial quantity = x litres
Initial quantities:
A = (6/20)x liters; B = (9/20)x liters; C = (5/20)x liters
A drained = (6/20) × 30 = 9 litres
B drained = (9/20) × 30 = 13.5 litres
C drained = (5/20) × 30 = 7.5 litres
So, [(9/20)x - 13.5] - [(6/20)x - 9 + 12] = 18
⇒ (3/20)x - 16.5 = 18
⇒ (3/20)x = 34.5
⇒ x = 34.5 × (20/3) = 230 litres