**Averages**

**[1-2 Questions]**

This section contains questions based on Average Height/Weight/Marks/Age, Average Temperature, Average Money expenditure, etc. The candidate needs to know only a single formula to solve these questions i.e.

**Average = (Sum of Quantities)/ (Number of Quantities)**

Suppose there are three numbers 1, 2, 3 then their average will be (1 +2 + 3) / 3 = 2.

**Example 1:**

**Find the average of X and Y if 30X + 30Y = 600.**

**30**- 60
- 70.5
- 10
- None of these

**Answer:** (4)

**Solution:**

30 (X+Y) = 600

=>X+Y = 20

So the average is 20/2 = 10.

**Example 2:**

**If the average of 50 numbers is 0, then at least how many numbers has to be Zero?**

**1**- 5
- 9
- 2
- None of these

**Answer: **(1)

**Solution:**

Since there are 50 numbers and the average is given as 0, so the sum of the numbers has to be 0. Here the 49 numbers can be positive with a sum of ‘x’ and the last number can be ‘-x’. So the least negative number is 1.

**Tip: **A good practice will ensure faster and efficient calculation.

**Percentages**

**[1-2 Questions]**

Basic percentage related questions are asked in this section. These questions will be based on comparisons.

Percentage is nothing but a rate, or number, or amount in each hundred.

This means 30% of something is 30 / 100 = 0.3 of that.

So 30% of any number, suppose 50, is 50 * 0.3 = 15.

**Example:**

**Ronit has some pens. He loses 60% of those pens and still has 80 pens left. How many pens did he originally have?**

**200**- 234
- 234
- 234
- None of these

**Answer:** (1)

**Solution:**

Let x be his original pens

So, (100 – 60) % of x = 80

40% of x = 80

=> x = 80 **÷** 0.4 = 200 pens.

**Tip:**

The best way to do the percentage problems is to consider the percent in terms of 100.

Suppose a question is asked as “What is 40% of 50?” This can easily be done if 50 is considered as 100 and so 40% of 100 is always 40. Now divide 40 with 2 since we had already multiplied 50 with 100. This gives the answer as 20.

**Ratio and Proportions**

**[1-2 Questions]**

These questions will be based on simple and compound ratios, componendo and dividendo, proportions. Ratios can be simply understood as the comparisons between values and proportions can be understood as equal ratios between two quantities.

If there are 2 dogs and 3 cats, then we can say that the ratio of dogs and cats is 2 : 3.

Now if there are 4 dogs and 6 cats, still the ratio remains same i.e. 2 : 3. So we can say that the number of dogs and cats increased proportionally.

**Example:**

**Rahul and Sourav earn 30% and 60% more than Ravi. The ratio of the earnings of Rahul and Sourav is:**

**1: 2**- 13: 16
- 16: 13
- 4: 3
- None of these

**Answer:** (3)

**Solution:**

Let Ravi’s earning be x

Then Rahul’s earning = 130% of Ravi = (130/100) × x

And Sourav’s earning = 160% of ravi = (160/100) **×** x

So the ratio will be 13: 16.