A can contains a mixture of two liquids A and B in proportion 7:5. When 9…
2024
A can contains a mixture of two liquids A and B in proportion 7:5. When 9 litres of mixture was drawn off and the can was filled with B, the proportion of A and B becomes 1:2. How many litres of mixture was contained by the can initially?
- A.
15
- B.
18
- C.
19
- D.
21
Attempted by 8 students.
Show answer & explanation
Correct answer: D
Let the total capacity be x litres.
Initially, A = 7/12 × x and B = 5/12 × x.
When 9 L of mixture is removed, A removed = 9 × 7/12 = 63/12 and A remaining = 7x/12 − 63/12 = (7x − 63)/12.
B after removal = 5x/12 − 9 × 5/12 = (5x − 45)/12. After adding 9 L of B, final B = (5x − 45)/12 + 9 = (5x + 63)/12.
Given final ratio A:B = 1:2, so 2 × A_final = B_final. Therefore 2 × (7x − 63)/12 = (5x + 63)/12.
Solve: 2(7x − 63) = 5x + 63 ⇒ 14x − 126 = 5x + 63 ⇒ 9x = 189 ⇒ x = 21.
Therefore the initial capacity of the can was 21 litres.