**Worksheet on Word Problems on Percentage 3 : **

This is the continuity of our web content given on "Word problems on Percentage Worksheet 2".

Before we look at the problems, if you want to know the shortcuts required for solving percentage problems,

**Problem 1 :**

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 2 :**

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

**Problem 3 : **

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

**Problem 4 :**

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

**Problem 5 :**

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

**Problem 1 :**

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 = 120 ⋅ 3 = $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

**Problem 2 :**

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 |
aaaaaaaaaaaaaaaaaaaaaaa aaa Profit % = 8% |

**Problem 3 : **

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%

**Problem 4 :**

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 ⋅ 8 articles = 5 ⋅ 15 = $75

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

**Selling price :**

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

40 articles = 4 ⋅ 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.

**Problem 5 :**

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 = 15 ⋅ 1 = $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%

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