Q141
ArithmeticRatio, Proportion & Mixtures
In a mixture, ratio of first and second liquid is $2:3$ and in another mixture ratio of those two liquids is $5:4$. Ratio in which the two mixtures be mixed so that quantity of two liquids in the new mixture be equal is
- a.2:5
- b.3:7
- c.5:9
- d.9:11
Answer: (C) 5:9
In the first mixture liquid 1 is $\tfrac{2}{5}$ and in the second it is $\tfrac{5}{9}$; in the final mixture it must be $\tfrac{1}{2}$. By alligation, first : second $= \left(\tfrac{5}{9}-\tfrac{1}{2}\right) : \left(\tfrac{1}{2}-\tfrac{2}{5}\right) = \tfrac{1}{18} : \tfrac{1}{10} = 5:9$. Check: taking 5 litres and 9 litres gives liquid 1 $= 2+5 = 7$ and liquid 2 $= 3+4 = 7$, which are equal.