# WORD PROBLEMS ON PERCENTAGE WORKSHEET

Problem 1 :

A product is sold for \$96 with a profit of 20%. Find the cost price of the product.

Problem 2 :

If the profit is 10%, then the selling price is \$132. If the profit is 15%, what must be the selling price?

Problem 3 :

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

Problem 4 :

There are 15 boys and 12 girls in a section A of class 7. If 3 boys are transferred to section B of class 7,then find the percentage of boys in section A.

Problem 5 :

If there are 3 boys and 7 girls in a class then, what percent of the class is made up of boys?

Problem 6 :

Two numbers are respectively 20% and 50% are more than a third number, Find the the ratio of the two numbers.

Problem 7 :

In a triangle, the first angle is 20% more than the third angle. Second angle is 20% less than the third angle. Then find the three angles of the triangle.

Problem 8 :

A trader cheats his customer to make a profit by stating that he sells at cost price but gives his customers only 800 grams. for every 1000 grams. What is his profit percentage?

Problem 9 :

A sells to B an item at 15% profit. B sells the same item to C at 20% profit. If C pays \$1656 for it, find the price at which A bought the item.

Problem 10 :

Mr. Lenin sold a chair at a loss of 15%. If he had sold at a profit of 10%, he would have got \$100 more. What is the cost is the cost price of the chair?

Problem 11 :

If good are purchased for \$ 1500 and one fifth of them sold at a loss of 15%. Then at what profit percentage should the rest be sold to obtain a profit of 15%?

Problem 12 :

By selling 20 articles, a trader gained the selling price of 5 articles. Find the profit percent.

Let x be the cost price of the product.

Given : When the profit is 20%, the selling price is \$96.

(100 + 20)% of x = 96

120% of x = 96

1.2x = 96

Divide both sides by 1.2

x = 80

The cost price of the product is \$80.

To answer this question, first we have to know the cost price of the product.

Let x be the cost price.

Given : When the profit is 10%, the selling price is \$120.

(100 + 10)% of x = 132

110% of x = 132

1.1x = 132

Divide each side by 1.1.

x = 120

The cost price of the product is \$120.

If the profit is 15%, then the selling price is

= (100 + 15)% of the cost price

= 115% of the cost price

= 1.15  120

= 138

When the profit is 15%, the selling price is \$138.

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

Let 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 x  = 9 ----(1) ----> incorrect

15 x ⁵⁄₃ = 25 ----(2) ----> correct

Difference between (1) and (2) is 16.

Percentage error is

= (Actual error/Correct answer) ⋅ 100%

= (16/25)  100%

= 64%

Before transfer :

No. of boys in section A = 15

No. of boys in section B = 12

Given : 3 boys are transferred from section A to B.

After transfer :

No. of boys in section A = 12

No. of boys in section B = 12

Hence,  percentage of boys in section A is 50%.

Total number of students in the class :

= 3 + 7

= 10

Percentage of boys is

= (No. of boys/Total no. of students)  100%

= ³⁄₁₀  100 %

= 30%

Let x be the third number.

First number :

= (100 + 20)% of x

= 120% of x

= 1.2x

Seocnd number :

= (100 + 50)% of x

= 150% of x

= 1.5x

Ratio between the first number and second number :

= 1.2x : 1.5x

Multiply both the terms of the ratio by 10 to get rid of the decimal point.

= 12x : 15x

Divide both the terms of the ratio by 3x.

= 4 : 5

Let x be the third angle.

First angle = 120% of x

= 1.2x

Second angle = 80% of x

= 0.8x

Sum of the three angles in a triangle = 180°

x + 1.2x + 0.8x = 180°

3x = 180°

Divide both sides by 3.

x = 60°

First angle :

= 1.2(60°)

= 72°

Second angle :

= 0.8(60°)

= 48°

Hence, the three angles of the triangle are 72°, 60° and 48°.

Cheated Value = 1000 - 800 = 200.

False weight = 800.

Profit percemntage :

= (Cheated value/False weight) ⋅ 100%

= (²⁰⁰⁄₈₀₀⋅ 100%

= 0.25 ⋅ 100%

= 25%

Hence, the price at which A bought the item is \$1200.

Let x be the cost price of the chair.

S.P (-15%) = 85% of x

= 0.85x ----(1)

S.P (+10%) = 110% of x

= 1.1x ----(2)

In (2), he got \$100 more than (1).

(2) - (1) = 100

1.1x - 0.85x = 100

0.25x = 100

25x = 10000

Divide both sides by 25.

x = 400

Hence, the cost price of the chair is \$400.

As per the question, we need 15% profit on \$1500.

Selling price for 15% on 1500.

S.P = 115%  1500

= 1.15 ⋅ 1500

= 1725

When all the good sold, we must have received \$1725 for 15% profit.

When we look at the above picture, in order to reach 15% profit overall, the rest of the goods (\$1200) has to be sold for \$1470.

That is,

C.P = \$1200, S.P = \$1470, Profit = \$270

Profit percentage :

²⁷⁰⁄₁₂₀₀  100%

= 0.225  100%

= 22.5%

Hence, the rest of the goods to be sold at 22.5% profit in order to obtain 15% profit overall.

Let x be the seling price of 5 articles.

Selling price of 20 articles :

= 4 ⋅ (selling price of 5 articles)

= 4 ⋅ x

= 4x

Given : Profit of 20 articles = Selling price of 5 articles.

Profit of 20 articles = x

Cost price of 20 articles :

= Selling price of 20 articles - Profit of 20 articles

= 4x - x

= 3x

Profit percentage :

ˣ⁄₃ₓ ⋅ 100%

⋅ 100%

33.33%

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