WORD PROBLEMS ON PERCENTAGE

Problem 1 :

John paid $64 for an item after 20% discount. Find the price of the item without discount. 

Solution :

Let x be the price of the item without discount. 

Given : John paid $64 for the item after 20% discount.

Then, we have

(100 - 20)% of x  =  64

0.8x  =  64

Divide each side by 0.8

x  =  80

So, the price of the item without discount is $80.

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%. 

Apart from the problems on percentage given above, if you need more problems on percentage, please click the following links. 

Percentage Word Problems - 1

Percentage Word Problems - 2

Percentage Word Problems - 3

Percentage Word Problems - 4

Percentage Word Problems - 5

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