A cistern contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of the mixture is drawn off and replaced with liquid B, the ratio of A to B becomes 7 : 9. Find the initial quantity of A (in litres).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 21
The 9 litres drawn off carry A and B in the ratio 7 : 5; then 9 litres of B goes back. Writing the new amounts in terms of the original multiplier gives one equation.
Initially A \(=7k\), B \(=5k\) litres
9 litres drawn off contain A \(\displaystyle =\frac{7}{12}\times9=\frac{21}{4}\) and B \(\displaystyle =\frac{15}{4}\)
After refilling: A \(\displaystyle =7k-\frac{21}{4}\), B \(\displaystyle =5k-\frac{15}{4}+9=5k+\frac{21}{4}\)
\(\displaystyle 9\left(7k-\frac{21}{4}\right)=7\left(5k+\frac{21}{4}\right)\)
\(\displaystyle 63k-\frac{189}{4}=35k+\frac{147}{4}\), so \(28k=84\) and \(k=3\)
Initial A \(=7\times3=21\) litres
The cistern had 21 litres of A at the start.