CAT The Calculation of a ratio: Percentage and decimal values - Practice Questions & MCQ
Quick Facts
-
5 Questions around this concept.
Solve by difficulty
EASYIn a mixture of 45 litres, the ratio of milk and water is 3 : 2. How much water must be added to make the ratio 9 : 11?
Give that 24 Carat gold is pure gold. 18 Carat gold is$\frac{3}{4}$ pure gold and 20 carat gold is $\frac{5}{6}$ pure gold. The ratio of the pure gold in 18 carat gold to the pure gold in 20 carat gold is:
In three similar vessels, the ratio of water and milk is 6:7, 5:9, and 8:7, respectively. If the mixtures of the three vessels are mixed together, then what will be the ratio of water and milk?
Three containers of capacity 20L, 5L, and 9L contain a mixture of milk and water with milk concentrations of 90%, 80%, and 70%, respectively. The contents of three containers are emptied into a large vessel. What is the approximate ratio of milk to water in the resultant mixture?
Concepts Covered - 1
Definition:
A ratio is a comparison between two quantities, showing the relative size of one quantity to another. It is often expressed in the form `a:b`, where "a" and "b" are the two quantities.
Converting Ratio to Percentage:
Given a ratio `a:b`, the percentage representation of "a" in terms of the whole (a+b) is given by:
Converting Ratio to Decimal:
Given a ratio `a:b`, the decimal representation of "a" in terms of the whole (a+b) is:
Foundation Building Questions:
Question:
The number of male employees in a company is in the ratio 7:3 to the number of female employees. If the number of male employees is 105, find the percentage of female employees.
Solution:
Given ratio of male to female employees = 7:3
Number of male employees = 7x
Number of female employees = 3x
Given 7x = 105
=> x = 15
Number of female employees
Total employees
Percentage of female employees
Tips and Tricks:
1. Cross-Multiplication: This method is handy to quickly compare two ratios. If you have two ratios a:b and c:d, you can compare them by looking at the products ad and bc. If ad > bc, then the ratio a:b is greater.
2. Unitary Method: If you have the ratio and one of the actual values, always find the value of 1 unit first (as shown in the previous year question's solution). It simplifies calculations and can be applied uniformly to most problems.
3. Percentage and Decimal: Remember, ratios give a relationship between two parts. Percentages and decimals give the proportion of one part to the whole. Switching between these can provide insights into many questions.
4. Break Down Complex Ratios: If given a complex ratio such as 2:3:4, and you know the total or one part, break it down into simpler ratios (with respect to one part) to make calculations more straightforward.
When studying and practising, make sure to regularly solve problems from previous years. This helps in understanding the pattern and nature of questions, making the actual exam more approachable.
"Stay in the loop. Receive exam news, study resources, and expert advice!"
