Question : Two jars A and B contain the solutions of two liquids P and Q. The ratio of the liquids P and Q in jars A and B are 2 : 19 and 1:11, respectively. If 7 litres of the solution of jar A and 4 litres of the solution of jar B are mixed, what is the ratio of the solutions P and Q in the new mixture?
Option 1: 10 : 1
Option 2: 1 : 9
Option 3: 9 : 1
Option 4: 1 : 10
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Correct Answer: 1 : 10
Solution :
| The ratio in the mixture | Amount of P | Amount of Q | |
| 7 | A (2 : 19) | $\frac{2}{21}\times7$ | $\frac{19}{21}\times7$ |
| 4 | B (1 : 11) | $\frac{1}{12}\times4$ | $\frac{11}{12}\times4$ |
⇒ $P:Q=(\frac{2}{21}\times7+\frac{1}{12}\times4):(\frac{19}{21}\times7+\frac{11}{12}\times4)$
⇒ $P:Q=(\frac{2}{3}+\frac{1}{3}):(\frac{19}{3}+\frac{11}{3})$
⇒ $P:Q=\frac{2+1}{3}:\frac{19+11}{3}$
$\therefore P: Q=3:30=1:10$
Hence, the correct answer is 1 : 10.
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