**Word Problems on Percentage : **

In this section, we are going to learn, how to solve percentage word problems step by step.

Before we look at the problems, if you want to know the shortcuts required for solving percentage problems,

**Problem
1 :**

What is 20% of 50 ?

**Solution
:**

20 % of 50 = 0.2 ⋅ 50 = 10

Hence, 20% of 50 is 10

**Problem
2 :**

If A's salary is 20% less than B's salary. By what percent is B's salary more than A's salary ?

**Solution
:**

Let us assume B's salary = $100 ----------(1)

Then, A's salary = $80 --------(2)

Now we have to find the percentage increase from (2) to (1).

Difference between (1) and (2) = $ 20

Percentage increase from (2) to (1) is

= (20/80) ⋅ 100%

= 25%

Hence, B's salary is 25% more than A's salary.

**Problem
3 :**

In an election, a candidate who gets 84% of votes is elected by majority with 588 votes. What is the total number of votes polled ?

**Solution
:**

Let "x" be the total number of votes polled.

Given : A candidate who gets 84% of votes is elected by majority of 476 votes

From the above information, we have

84% of x = 588 ---------> 0.84x = 588

x = 588 / 0.84

x = 700

Hence, the total number of votes polled 700.

**Problem
4 :**

When the price of a product was decreased by 10 % , the number sold increased by 30 %. What was the effect on the total revenue ?

**Solution :**

Before decrease in price and increase in sale,

Let us assume that price per unit = $100.

Let us assume that the number of units sold = 100

Then the total revenue = 100 ⋅ 100 = 10000 --------(1)

After decrease 10 % in price and increase 30 % in sale,

Price per unit = $ 90.

Number of units sold = 130

Then the total revenue = 90 ⋅ 130 = 11700 --------(2)

From (1) and (2), it is clear that the revenue is increased.

Difference between (1) and (2) = 1700

Percent increase in revenue is

= (Actual increase / Original revenue) ⋅ 100 %

= (1700/10000) ⋅ 100 %

= 17 %

Hence, the net effect in the total revenue is 17% increase.

**Problem 5 :**

A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation ?

**Solution :**

In the given two fractions, the denominators are 5 and 3.

Let us assume a number which is divisible by both 5 and 3.

Least common multiple of (5, 3) = 15.

So, let the number be 15.

15 ⋅ 3/5 = 9 ----------(1) ---------incorrect

15 ⋅ 5/3 = 25 ---------(2) --------correct

Difference between (1) and (2) is 16

Percentage error is

= (Actual error/Correct answer) ⋅ 100 %

= (16 / 25) ⋅ 100 %

= 64%

Hence, the percentage error in the calculation is 64%.

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