HOW TO SOLVE PERCENTAGE PROBLEMS IN APTITUDE EASILY

Problem 1 :

The price of a product is $80. If the price is increased by 25%, find the new price.

Solution :

The new price :

= (100 + 25)% of $80

= 125% of $80

= 1.25 ⋅ $80

= $100

Problem 2 :

The price of a product is $120. If the product is sold at 10% discount, find the price price of the product after discount.

Solution :

The price of the product after discount :

= (100 - 10)% of $120

= 90% of $120

= 0.90 ⋅ $120

= $108

Problem 3 :

A store buys a camara for $250. If the store wants to earns 12% profit, at what price should the store sell the camara?

Solution :

Selling price of the camara : 

= (100 + 12)% of $250

= 112% of $250

= 1.12 ⋅ $250

= $280

Problem 4 :

A product was bought for $30 and sold for $36. Find the profit percentage.

Solution :

Profit percentage :

= ⁽³⁶ ⁻ ³⁰⁾⁄₃₀ ⋅ 100%

= ⁶⁄₃₀ ⋅ 100%

= ⁶⁄₃₀ ⋅ 100%

= ⅕ ⋅ 100%

= 20%

Problem 5 :

A product was bought for $90 and sold for $63. Find the loss percentage.

Solution :

Loss percentage :

= ⁽⁹⁰ ⁻ ⁶³⁾⁄₉₀ ⋅ 100%

= ²⁷⁄₉₀ ⋅ 100%

= ³⁄₁₀ ⋅ 100%

= 30%

Problem 6 :

The cost price of a product is $55. If the product is sold at a profit of 5%, find the selling price.

Solution :

selling price = (100 + 5)% of cost price

selling price = 105% of cost price

selling price = 1.05 ⋅ cost price

Substitute 55 for cost price.

selling price = 1.05 ⋅ 55

selling price = $57.75

Problem 7 :

The cost price of a product is $70. If the product is sold at a loss of 10%, find the selling price.

Solution :

selling price = (100 - 10)% of cost price

selling price = 90% of cost price

selling price = 0.9 ⋅ cost price

Substitute 70 for cost price.

selling price = 0.9 ⋅ 70

selling price = $63

Problem 8 :

The selling price of a product is $99. If there is 20% profit on selling the product, find the cost price.

Solution :

selling price = (100 + 20)% of cost price

selling price = 120% of cost price

selling price = 1.2 ⋅ cost price

Substitute 99 for selling price.

99 = 1.2 ⋅ cost price

Divide both sides by 1.2.

cost price = $82.50

Problem 9 :

The selling price of a product is $152. If there is 5% loss on selling the product, find the cost price.

Solution :

selling price = (100 - 5)% of cost price

selling price = 95% of cost price

selling price = 0.95 ⋅ cost price

Substitute 152 for selling price.

152 = 0.95 ⋅ cost price

Divide both sides by 0.95.

cost price = $160

Problem 10 :

The second angle of a triangle is 20% more than the first angle. The third angle is 2° less than 120% of the second angle. Find the angles of the triangle.

Solution :

Let x be the first angle.

second angle = (100 + 20)% of x

= 120% of x

= 1.2x

third angle = 120% of 1.2x - 2°

= 1.2(1.2x) - 2°

= 1.44x - 2°

sum of the angles of a triangle = 180°

x + 1.2x + 1.44x - 2° = 180°

3.64x - 2° = 180°

Add 2° to both sides.

3.64x = 182°

Divide both sides by 3.64.

x = 50°

fist angle = 50°

second angle = 1.2(50°)

= 60°

third angle = 1.44(50°) - 2°

= 72° - 2°

= 70°

The angles of the triangle are 50°, 60° and 70°.

Problem 11 :

There are 720 students in a school and 40% of the students are boys. If 62 new boys and 12 new girls are admitted, find the percentage of boys.

Solution :

Number of boys in the school :

= 40% of 720

= 0.4 ⋅ 720

= 288

Number of girls in the school :

= 720 - 288

= 432

After new admission,

number of boys = 288 + 62 = 350

number of girls = 432 + 12 = 450

total number of students = 350 + 450 = 800

Percentage of boys in the school after new admission :

= ³⁵⁰⁄₈₀₀ ⋅ 100%

= 0.4375 ⋅ 100%

= 43.75%

Problem 12 :

A is 20% of B and B is 40% of C. What percentage of A is C?

Solution :

Given : A is 20% of B and B is 40% of C.

A = 0.2B ----(1)

B = 0.4C

Substitute B = 0.4C in (1).

A = 0.2(0.4C)

A = 0.8C

Divide both sides by 0.8.

ᴬ⁄₀.₈ = C

(¹⁄₀.₈)A = C

1.25A = C

125% of A = C

Problem 13 :

A is 10% more than B and B is 20% more than C. A is what percentage more than of C?

Solution :

Given : A is 10% more than B and B is 20% more than C.

A = (100 + 10)% of B

A = 110% of B

A = 1.1B ----(1)

B = (100 + 20)% of C

B = 120% of C

B = 1.2C

Substitute B = 1.2C in (1).

A = 1.1(1.2C)

A = 1.32C

A = 132% of C

A = (100 + 32%) of C

A is 32% more than C

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