**Word Problems on Percentage 2 : **

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 :**

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?

**Solution :**

Cheated Value = 1000 - 800 = 200

False weight = 800

Profit % = (Cheated value/False weight) ⋅ 100%

Profit % = (200/800) ⋅ 100%

Profit % = 25%

**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, find the price at which A bought the item.

**Solution :**

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

**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

= 0.85x --------(1)

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

= 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.

**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 = 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

Profit percentage = 22.5 %

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

**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% = (1/3) ⋅ 100%

Profit percentage = 33.33%

Hence, the profit percentage is 33.33.

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