Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
Two identical vessels A and B contain mixtures of milk and water in the ratios 4 : 5 and 5 : 1 respectively. In what ratio should quantities of mixtures be taken from A and B to form a mixture in which milk to water is in the ratio 5 : 4? 4 5
Answer
Answer (as printed):
Explanation
Milk in $A=\frac{4}{9}$ units; Milk in $B=\frac{5}{6}$ units; Water in $A=\frac{5}{9}$ units; Water in $B=\frac{1}{6}$ units. Let $A$ and $B$ be taken in the ratio $1:y$. Then, $\frac{\frac{4}{9}+\frac{5y}{6}}{\frac{5}{9}+\frac{y}{6}}=\frac{5}{4} \Rightarrow \frac{8+15y}{10+3y}=\frac{5}{4}$ $$\Rightarrow 4(8+15y)=5(10+3y) \Rightarrow 32+60y=50+15y \Rightarrow 45y=18 \Rightarrow y=\frac{2}{5}.$$ $$\therefore \quad \text{Required ratio}=1:\frac{2}{5}=5:2.$$
Explanation as extracted from the printed page; notation may be imperfect.