# Percentage Aptitude Problems

## Percentage Aptitude Problems Tips and Tricks

In mathematics, a **Percentage** is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

Rule : If x % of a quantity is taken by the first person, y % of the remaining quantity is taken by second person and z % of the remaning is taken by third person. If P amount is left in the balance, then original amount Q will be.

## Solution

Q = (P * 100 * 100 * 100) / (100-X) (100-Y) (100-Z)

If x % of a quantity is added, again y % of the increased quantity is added, again z % of the increased quantity is added, now it becomes P then the origial quantity Q is given by

## Solution

Q = (P * 100 * 100 * 100) / (100+X) (100+Y) (100+Z)

If P is the original population of a town and annual increase is r % then Population after one year will be

## Solution

P + Pr/100 - P(1+ r/100)

**Question 1: **The total population of a city is 6500.The number of males and females increases by 5 % and 10 % respectively and consequently the population becomes 7000. Find the number of males in the village.

**(A)**4000**(B)**3000**(C)**3500**(D)**2950

**Answer: **(B) 3000

## Solution

We are given that, 1) Total population of city = 6500 2) Increase in male and female population = 5 % & 10% respectively. 3) Final population of city = 7000 Hence, Let's assume that number of males = x Number of female = 6500 – x Therefore, after increase in 5 % male and 10 % female, the population becomes 7000 5 % male +10 % female = Difference between new and original population (5/100)*x + 10/100(6500 – x) = 7000 – 6500 5x+65000-10x=50000 5x= 15000 x=3000 Number of males = 3000 Number of females = 3500

**Question 2: **A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

**(A)**588 apples**(B)**600 apples**(C)**672 apples**(D)**700 apples

**Answer: **(D) 700 apples

## Solution

Suppose originally he had x apples. Then, (100 - 40)% of x = 420. =60/100*X=420 X=(420*100)/60=700

**Question 1: **What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

**(A)**1**(B)**14**(C)**20**(D)**21

**Answer: **(C) 20

## Solution

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. Number of such number =14 Required percentage = (14/70)*100 = 20%

**Question 3: **The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

**(A)**4.37%**(B)**5%**(C)**6%**(D)**8.75%

**Answer: **(B) 5%

## Solution

Increase in 10 years = (262500 - 175000) = 87500. Increase% = (87500/175000)*100 = 50% Required average = (50/10) = 5%

**Question 4: **In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?

**(A)**150**(B)**20**(C)**120**(D)**100

**Answer: **(D) 100

## Solution

Let the number of students be x. Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x. 80% of x = 48 + 2/3 of 48 80/100 X = 80 X = 100