## Percentage problems and solutions for aptitude

**Percent** means per hundred. Percentages are way of expressing hundredth. So ‘X ” *percent* means X per hundred or ” X/100 “. The concept of *percentage* mainly applies to ratios, and the percentage value of ratio is arrived at by multiplying by 100 the decimal values of ratio.

**Percentage calculation** plays very important role in the **quantitative aptitude**. Because some other topics in **QA** also depended on the *percentage calculation*.

Percentage formulas for different types of applications were already given the below like.

General Percent formulas | Net change of a number while percentage increase or decrease | Net percent change in area of circle or square.

In this page explained about some more examples with shortcut tricks on **percentage calculation.**

**Example 1 : **In trader gives successive discounts of 10%, 20% and 30% respectively. Then find percentage of the original coast price he will recover?

**Solution :** Its having the two methods and by using formula

**Direct method :** Take 100

100 x (100-10)% = 90 ( 10% discount ).

90 x (100 – 20)% = 72 ( 20% discount ).

72 x ( 100-30) % = 50.4 ( 30% discount ).

Hence overall discount 49.6 % and the answer is 50.4%.

**By using formula :**

Take 10% and 20% discounts

i.e -10 – 20 + (10 x 20 /100 ) = -28% ( i.e Negative sign means 28% discount )

Take 28% and 30% discounts

i.e -30 – 28 + (30 x 28 /100 ) = – 49.6% ( i.e overall discount 49.6 % discount)

Our final answer is 50.4 % ( 100%-49.6% = 50.4%).

**Example 2 : **A person salary increased 20% and then deceased by 20%. What is the net percentage change in his salary?

**Solution : Here remember one tip ” The net percent always decreased when same percent increased then decreased or same percent decreased then increased”.**

By using formula **(x / 10) ^{2 }**Here take x = 20

= **(20 / 10) ^{2}** = 4 % decreased.

**Example 3 : **” A’s ” salary is 50% more than B’s salary. By what percent is B ‘s salary less than A’s salary?

Sol: Take B’s salary 100 then A’s salary is 150. ( Due to 50% more ).

Now using the formula

= (1/3) x 100 = 33.33%

So B ‘s salary 33.33% less than A’s salary**.**

**Example 4 :** The length and the breadth of a rectangle are changed by +20% and by -10% respectively. What is the percentage change in the area of the rectangle?

Sol : Direct method

( 100 + 20) x ( 100 – 10) = 120 x 90 = 108%.

So area increased by 8%

Now by using formula

= 20 – 10 – 2 = 8% ( here comes positive value so it will be increased)

So area increased by 8%.

**Example 5 :** A’s salary is 30% lower than B’s salary, which is 20% lower than C,s salary. By how much percent is C’s salary more than A’s salary?

Here Take C’s salary 100 then B’s salary 100 x ( 100-20)% = 80

Now A’s salary 80 x (100-30)% = 80 x 70% = 56.

Now using the formula = X is what percent greater than Y ( here x = 100 and y = 56 )

[ (100-56) / 56 ] x 100 = 44 x 100 / 56 = 78.57%

So C salary 78.57% more than A’s salary.

For the above sum we can using one shortcut method

Lower means take negative sign for for 30% and 20%.

i. e -30 -20 + (30 x 20 / 100 ) = -44%

So A’s salary 44% less than C salary. If take C’ s salary 100 than A’s salary having 56.

**Example 6 :** The cost of manufacturing of a medicine is made up of four components A, B , C and D which have ratio of 4 : 3 : 1 : 6 respectively. If there are respective changes in the cost of +20% , -10% , -30% and +30%, then what would be the percentage change in cost.

**Solution:** Here we using one shortcut i.e + 20% = 1.2 , -10% = 0.9 , -30% = 0.7 , +30% = 1.3

Assume the ratio value for single medicine = 4 + 3 + 1 + 6 = 14

Now calculate the new cost for the medicine = (4 x 1.2) + (3 x 0.9) + (1 x 0.7) + (6 x 1.3)

= 4.8 + 2.7 + 0.7 + 7.8 = 16.

Now calculate the percentage change

= [ (16-14) / 14 ] x 100 =2 x 100 / 14 = **14.29%.**

**Example 7 :** 30% of a number when subtracted from 91, gives the number itself. .Find the number?

Sol: Take the number ” X ” . 30% of ‘”X ” is 0.3X

Now 0.3X subtracted from 91 then comes ” X”

i.e 91 – 0.3X = X

**X = 70. **

**Example 8 :** Tom’s salary is 60% more than Ramki’s salary. Tom got a raise of 50% on his salary while Ramki got a raise of 20% on his salary. By what percent is Tom’s salary more than Ramki’s salary ?

Sol: Take Ramki’s salary 100 then Tom’s salary having 160.

Tom raise in his salary 50% . So Tom’s salary = 160 x 1.5 = 240.

Ramki raise in his salary 20% . So Ramki’s salary = 100 x 1.2 = 120.

Now calculate 240 what percent more than 120

= [ (240-120) / 120 ] x 100 = 120 x 100 / 120 = **100%.**

**Example 9 :** If 65 % of ” N ” = 13% of ” M”, then find the value of “N” if “M” = 1000.

Sol: 65 % of ” N means 0.65N and 13% of ” M” means 0.13M

So if M = 1000 then

0.65 x N = 0.13 x 1000

N = 200.

**Example 10 :** The difference of two numbers is 40% of the large number. If the smaller number is 120, then find the large number?

Sol: Take large number ” x ” and smaller number “y ‘

According to given logic.

The difference of “x” and “y ” is 40% of the” x”.

x – y = 0.4x

Here take y = 120 then x = 200.

**Example 11 :** The price per unit of article decreases by 20%. By what percentage should the consumption be increased such that expenditure remain the same?

Sol: Using the formula [ x / (100- x) ] x 100

Here x = 20%

So [ 20 / (100- 20) ] x 100 = 25%

**Example 12 :** A person spends 25% of his salary on food , 15% on house rent, 38% on miscellaneous. If the savings at the end of a month is $880, then find his total salary?

Sol: Take total salary = X

then X = 0.25X + 0.15X + 0.38X + 880

X – 0.78X = 880

**X = $4000.**

#### Some more example with solutions on percentage calculation will be added shortly.

**Some related Topics in Quantitative aptitude**

The Concepts of number system the mathematics

Divisibility Rules of numbers from 1 to 20 | Basic math education

Simple interest and Compound interest formulas with examples

Percentage formulas | percentage calculations with examples

Circle formulas in math | Area, Circumference, Sector, Chord, Arc of Circle

Types of Quadrilateral | Quadrilateral formula for area and perimeter

Types of Triangles With examples | Properties of Triangle

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