**Solving percent problems :**

Percent means per hundred.

That is, the given number compared to 100.

For example,

17% = 17/100

In this section, we are going to see how to solve real world problems involving percents.

**Problem 1 : **

What 30 percent of 600 ?

**Solution : **

The picture given below clearly illustrates the answer for the given question.

Hence, 30 percent of 600 is 180.

**Problem 2 : **

What percent of 500 is 75 ?

**Solution : **

The picture given below clearly illustrates the answer for the given question.

Hence, 15 percent of 500 is 75.

**Problem 3 :**

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

**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% x 1500 = 1.15x1500 = **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.

**Problem 5 :**

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)x100 % = 44.44%

Hence the profit percentage is 44.44

**Problem 6 :**

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%

**Problem 7 :**

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 8 :**

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)x100 % = 4%

Hence, the loss percentage is 4.

After having gone through the stuff given above, we hope that the students would have understood "Solving percent problems".

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