Question : A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Option 1: $\frac{1}{3}$
Option 2: $\frac{1}{4}$
Option 3: $\frac{1}{5}$
Option 4: $\frac{1}{7}$
Correct Answer: $\frac{1}{5}$
Solution : Given: Suppose the vessel initially contains 8 litres of liquid. In this liquid, water is 3 litres and syrup is 5 litres. So the ratio is 3 : 5. Let $x$ litres of this liquid be replaced with water. Quantity of water in $x$ litre of liquid $=\frac{3x}{8}$ Quantity of syrup in $x$ litre of liquid $=\frac{5x}{8}$ As per given condition, The quantity of water in the new mixture is $=3-\frac{3x}{8}+x$ The quantity of syrup in the new mixture is $=5-\frac{5x}{8}$ After replacement, the quantity should be the same. $3-\frac{3x}{8}+x=5-\frac{5x}{8}$ ⇒ $\frac{5x}{8}-\frac{3x}{8}+x=2$ ⇒ $\frac{10x}{8}=2$ $\therefore x=\frac{8}{5}$ So, part of the mixture replaced $=\frac{\frac{8}{5}}{8}=\frac{8}{5}×\frac{1}{8}=\frac{1}{5}$ Hence, the correct answer is $\frac{1}{5}$.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : Three vessels whose capacities are 3 : 2 : 1 are filled with milk mixed with water. The ratio of milk and water in the mixture of vessels is 5 : 2, 4 : 1, and 4 : 1, respectively. Taking $\frac{1}{3}$ of first, $\frac{1}{2}$ of second, and $\frac{1}{7}$ of third mixtures,
Question : The value of $\frac{\frac{5}{2}-\frac{3}{7} \times 1 \frac{4}{5} \div 3 \frac{6}{7}}{\frac{3}{2}+1 \frac{2}{5} \div 3 \frac{1}{2} \times 1 \frac{1}{4}}$ is:
Question : In a mixture of 25 litres, the ratio of acid to water is 4 : 1. Another 3 litres of water is added. The ratio of acid to water in the new mixture is:
Question : A right cylindrical vessel is full of water. How many right cones with the same diameter and height as the right cylinder will be needed to store that water? (Take $\pi =\frac{22}{7}$ )
Question : What is the simplified value of: $7 \frac{1}{3} \div 2 \frac{1}{2}$ of $1 \frac{3}{5}-\left(\frac{3}{8}+\frac{1}{7} \times 1 \frac{3}{4}\right)-\frac{5}{24}$
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile