# WORD PROBLEMS ON PERCENTAGE - 3

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.

Percentage Word Problems

Percentage Word Problems - 1

Percentage Word Problems - 2

Percentage Word Problems - 4

Percentage Word Problems - 5

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