CAT Ratio comparison - Practice Questions & MCQ

Definition:

Ratio comparison involves determining the relation between two or more ratios, i.e., which one is greater, smaller, or if they are equal. It's essential to simplify the ratios to their lowest terms to effectively compare them.

How to Compare Ratios:

To compare the ratios a:b and c:d :

- Cross multiply the terms:

- a X d and b X c

- If ad > bc, then a:b > c:d

- If ad < bc, then a:b < c:d

- If ad = bc, then a:b = c:d

Foundation Building Questions:

Question:

A company’s ratio of production of gadgets in the years 2019 and 2020 was 5:6. In 2021, the company increased its production such that the ratio of production in 2020 to 2021 became 3:4. If the company produced 180 gadgets in 2020, how many gadgets were produced in 2019 and 2021?

Solution:

For 2019 and 2020, 

Ratio = 5:6

For 2020,

Let's assume 6x = 180 gadgets 

=> x = 30

For 2019, 

Gadgets produced = 5x = 5*30 = 150 gadgets

For 2020 to 2021, 

Ratio = 3:4

For 2021,

Using the unitary method (from Concept 1), if 3 units represent 180 gadgets, 

4 units = (180/3)*4 = 240 gadgets

Therefore, 

In 2019: 150 gadgets were produced.

In 2021: 240 gadgets were produced.

Tips and Tricks:

1. Simplify First: Before comparing, always simplify the given ratios to their lowest form. This avoids cumbersome calculations.

2. Sequential Ratios: Like in the above problem, ratios given in a sequence (one year after another) can often be solved by linking the common term. In the above problem, the production of 2020 was common.

3. Use Previous Concepts: As seen in the previous year question, always remember the unitary method from Concept 1 when you have one actual value and its corresponding ratio. It allows you to find other values quickly.

4. Plotting: For complex problems with sequential ratios spanning multiple years or stages, plotting the data on a rough chart or table can give a clearer picture.

5. Consistent Units: While comparing or working with ratios, ensure that all the units are consistent. If one ratio is given in kilograms and another in grams, convert everything to one consistent unit.

Using previous years’ questions for practice not only helps you understand the type of questions but also helps in identifying patterns, if any. This method of studying is beneficial for time management during the actual exam.