# Percentage (Aptitude) YouTube Lecture Handouts for Himachal Pradesh PSC

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Percentage Basics - 1 Key Trick (For Aptitude): Working and Thinking in Relative Quantities

## Key Ideas

Fractions, Rations and percent- relative quantities

Relative quantities and absolute quantities are not to be mixed.

Relative quantities can be added or subtracted

x represents the unknown in the relative quantity.

## If a = X% of Y and B = Y% of X, Then

X > Y

A > B

Y < X

A = B

## Percentage

There are verities of problems based on percentage. We would be covering basic concepts of today which is Basic Formula and Basic Concepts

Let us very briefly cover what percentage actually means.

This diagram clearly summarized the concept. Here there are total of 100 squares out of each 3 are sky. This fact is represents in several ways:

Fraction

Decimal

Percentage

In general

## Relative Quantities- Fractions, Rations & Percent

Similarly, this pizza that the slice represent no matter what the size of pizza.

Here, he had two blocks, in these particular bar I have total of 4 yellow, 2 brown and 2 red blocks.

Here each of red and brown and 2 of yellow.

Relative quantities of yellow, red and brown block in each of these two bars is same.

In smaller bars, quantities of red block and yellow block it represented as fraction

Ratio of the small bar in terms of red block

In same fact can be representing as percentage so, we want to convert of red blocks.

## Key Ideas

1. Fractions, ratios, and percent- relative quantities

2. Relative quantities and absolute quantities are not to be mixed.

3. Relative quantities can be added or subtracted

4. x represents the unknown in the relative quantity.

## What Percent is 60 of 240?

Total of 240 reduce 100.

Percent

## Find Sales Tax @ 20% from a Gross Figure of Rs. 1600?

## If 50% of of, then What Percent of is

Trick about this question is what percent of x is y:

## If 10% of a Number is Added with Itself then Result Becomes 1331. Find the Original Number

Here, we assume the relative number is it becomes

The original number is 1210.

## 60% of a Number is 360. What is 99% of the Same Number?

## If 15% of a Number is Subtracted from Itself then Result Becomes 2550. Find the Original Number

Here, 15 is subtracted is 85

## If 39 is Added in a Number, It Becomes 113 % of Itself. Find the Number

We assume that

Number added

## A House Sold for 357000 Dollars, Produces a Profit of 19%, Find the Profit?

Assume that the house

## 40% of 70 is What % More Than 30% of 80?

40% of 70

30% of 80

## A Fruit Seller Had Some Apples. He Sells 40% Apples and Still Has 420 Apples. Originally, He Had?

come out to be

So,

## If of Y and of X, Then

a.

b.

c.

d.

of Y

of X

So,

Hence,

## A Number Exceeds 20% of Itself by 40. Find the Number?

Assume the number and it self

## A Man Multiplied a Number by Instead of . What is % Error?

We assume that

We can assume,

Number by

## The Total Salary of a and B is Rs. 1500. A Spent 90% of His Income and B Spent 80% of His Income. The Ratio of Saving is 3:4. Find the Ratio of Their Salary. What is Their Absolute Salary?

We assume that A salary

B salary

A spent 90% so, A spent

B spent 80% so, B spent

If I have a Rs. 5, 3 would go to x and 2 would go to y.

We can multiply by 300 so,

and

Their absolute salary was .

## If a Exceeds B by, B is Less Than C by, then Is

Here,

## Next Class: % Change, Income & Consumption

The price of sugar decreases by 30%. By what % the consumption should increase so that expenditure decreases only by 10%?

A man spends Rs. 5700 from his income of Rs. 8550. If his income and expenditure are increased by 19% and 13%. Find the % change in saving?

-Mayank