**Worksheet on Word Problems on Percentage :**

Worksheet given in this section is much useful to the students who would like to practice word problems on percentage.

**Problem 1 :**

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 2 :**

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. What is the price at which A bought the item?

**Problem 3 :**

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 4 :**

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 5 :**

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

**Problem 6 :**

I purchased 120 books at the rate of $3 each and sold 1/3 of them at the rate of $4 each. 1/2 of them at the rate of $ 5 each and rest at the cost price. Find my profit percentage.

**Problem 7 :**

A trader marks his goods 20% above the cost price and allows a discount of 10% for cash. Find the profit percentage.

**Problem 8 :**

A person wants to get 20% profit after selling his object at 20% discount. Find the required percentage increase in marked price.

**Problem 9 :**

A person buys 8 articles for $15 and sells them at 10 for $18. Find the profit or loss percentage.

**Problem 10 :**

The selling price of 10 articles is the cost price of 15 articles. Find profit or loss percentage.

**Problem 1 :**

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.

**Solution :**

Let "x" be the third angle.

Then the first angle = 120% of x = 1.2x

The second angle = 80% of x = 0.8x

Sum of the three angles in any triangle = 180°

Then, we have x + 1.2x + 0.8x = 180°

3x = 180° --------> x = 60°

Then the first angle = 1.2(60°) = 72°

The second angle = 0.8(60°) = 48°

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

Let us look at the next problem on "Worksheet on word problems on percentage".

**Problem 2 :**

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. What is the price at which A bought the item?

**Solution :**

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

Let us look at the next problem on "Worksheet on word problems on percentage".

**Problem 3 :**

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?

**Solution :**

Let "x" be the cost price of the chair

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

S.P = 0.85x --------(1)

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

S.P = 1.1x ---------(2)

In (2), he got $100 more than (1). So we have

(2) - (1) = 100

1.1x - 0.85x = 100

0.25x = 100

25x = 10000

x = 400

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

Let us look at the next problem on "Worksheet on word problems on percentage".

**Problem 4 :**

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%?

**Solution :**

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

Selling price for 15% on 1500

S.P = 115% ⋅ 1500

S.P = 1.15 ⋅ 1500

S.P = 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) x 100

Profit percentage = 22.5 %

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

Let us look at the next problem on "Worksheet on word problems on percentage".

**Problem 5 :**

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

**Solution :**

Let "X" be the S.P of 5 articles.

Given : Profit of 20 articles = S.P of 5 articles

So, profit of 20 articles = X

S.P of 20 articles = 4 . (S.P of 5 articles) = 4X

C.P of 20 articles = S.P of 20 articles - Profit of 20 articles

C.P of 20 articles = 4X - X

C.P of 20 articles = 3X

Profit percentage = (X / 3X) ⋅ 100%

Profit percentage = (1/3).100%

Profit percentage = 33.33%

Hence, the profit percentage is 33.33

Let us look at the next problem on "Worksheet on word problems on percentage".

**Problem 6 :**

I purchased 120 books at the rate of $3 each and sold 1/3 of them at the rate of $4 each. 1/2 of them at the rate of $ 5 each and rest at the cost price. Find my profit percentage.

**Solution :**

Total money invested = 120x3 = $360 -------(1)

Let us see, how 120 books are sold in different prices.

From the above picture,

Total money received = 160 + 300 +60 = $ 520 --------(2)

Profit = (2) - (1) = 520 - 360 = $160

Profit percentage = (160/360) x 100% = 44.44%

Hence the profit percentage is 44.44

Let us look at the next problem on "Worksheet on word problems on percentage".

**Problem 7 :**

A trader marks his goods 20% above the cost price and allows a discount of 10% for cash. Find the profit percentage

**Solution :**

Let the cost price be $100.

Then, marked price (M.P) = $120

Let the selling price be "X"

From the above picture, we get

90% of (M.P) = X

(0.9).120 = X

108 = X --------> S.P = 108

Cost price = $100, Selling Price = $108

Profit % = 8%

Let us look at the next problem on "Worksheet on word problems on percentage".

**Problem 8 :**

A person wants to get 20% profit after selling his object at 20% discount. Find the required percentage increase in marked price.

**Solution :**

Let the cost price be $100.

Then, the selling price = $120

Let the marked price be "X"

From the above picture, we get

80% of (M.P) = S.P

(0.8)X = 120

X = 150 --------> M.P = 150

Cost price = $100, Marked Price = $150

Hence, the required percentage increase = 50%

Let us look at the next problem on "Worksheet on word problems on percentage".

**Problem 9 :**

A
person buys 8 articles for $15 and sells them at 10 for $18. Find the profit or loss percentage.

**Solution :**

**Cost price : **

8 articles -------> $15

40 articles = 5 x 8 articles = 5x15 = $75

C.P of 40 articles = $75 ----------(1)

**Selling price :**

10 articles -------> $18

40 articles = 4 x 10 articles = 4(18) = $72

S.P of 40 articles = $72 ----------(2)

From (1) and (2), we get C.P > S.P.

So there is loss.

And loss = (1) - (2) = 75 - 72 = 3

Loss percentage = (3/75) ⋅ 100 % = 4%

Hence, the loss percentage is 4.

Let us look at the next problem on "Worksheet on word problems on percentage".

**Problem 10 :**

The selling price of 10 articles is the cost price of 15 articles. Find profit or loss percentage.

**Solution :**

Let the cost price of one article be $1 -------(1)

Given :

S.P of 10 articles = C.P of 15 articles

S.P of 10 articles = 15x1 = $15

S.P of one article = 15/10 = $1.5 -------(2)

From (1) and (2), we get S.P > C.P

So, there is profit.

Profit = (2) - (1) = 1.5 - 1 = 0.5

Profit percentage = (0.5/1) ⋅ 100 = 50%

Hence, the profit percentage = 50%

After having gone through the stuff given above, we hope that the students would have understood "Worksheet on word problems on percentage"

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