**Word Problems on Percentage 3 : **

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

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.

**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

Total money received = $520 -----(2)

Profit = (2) - (1)

Profit = 520 - 360

Profit = $160

Profit percentage :

= (160 / 360) ⋅ 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

Therefore, the selling price is $108.

Cost price is $100 and the selling price is $108.

And the percentage increase from 100 to 108 is 8.

Hence, the profit percentage is 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 is $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

Therefore, the marked price is $150.

Cost price is $100 and the marked price is $150.

And the percentage increase from 100 to 150 is 50.

Hence, the required percentage increase is 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.

The loss is

= (1) - (2)

= 75 - 72

= 3

Loss percentage is

= (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 is C.P of 15 articles.

Then, we have

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%

Apart from the problems on percentage given above, if you need more problems on percentage, please click the following links.

After having gone through the stuff given above, we hope that the students would have understood, how to solve word problems on percentage.

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