**Profit and Loss with mathematical problems and solution**

## PROFIT

Profit is a remaining amount after total expenses costs are deducted from total revenue.

## LOSS

In a business Loss is the stage when total revenue cost is less than from the producing cost.

**COST PRICE**

The price which a customer or a shopkeeper pays for an article at the time of purchasing is called its cost price or prime cost.

**SELLING PRICE**

The price which a shopkeeper gets by selling an article is called its selling price.

Profit= Selling Price- Cost Price

=S.P-C.P

Loss= Cost Price- Selling Price

= C.P-S.P

Some way when a person decides to sell the article at a certain price e writes a price on the article above the selling price at which he wants to sell it. The price that he marks is known as marked price. He writes more price on the article because everyday asks for decreasing the price, which is written or marked. so decrease in price is known as discount.

Discount= Marked price- Selling price

At times 2 customers come for the same article , the shopkeeper sells the article above the marked price, the prices above the marked prices is known as premium.

Premium= Selling price- Marked price

**Profit and Loss**

These are always calculated on cost price.

Profit %= [(S.P-C.P)/C.P]*100

Loss%=[(C.P-S.P)/C.P]*100

**Formulae**

In case of Loss:

S.P.= C.P*(100-Loss%)/100

In case of gain:

S.P.= C.P*(100+Profit%)/100

In case of gain:

C.P.= S.P.*100/(100+Profit%)

In case of loss:

C.P.= S.P*100/(100-Loss%)

**Note**

- Profit and loss percent (%) is the gain or loss on every 100 of the cost price.
- If(S.P.)>(C.P), there is a gain.
- If (S.P.)< (C.P), there is a loss.
- If n successive discount at the rate of d1% ,d2%, d3%……..dn%, then

S.P=M.P.(1-d1/100)(1-d2/100)…..(1-dn/100)

where, M.P.= market price

**Example:**

Que: By selling a book for 200 rs a man gains 20 rs, what is his gain %

Ans:

We know that

P%= (Profit/C.P)*100

Cost Price= S.P-Profit

=200-20

=180

P%= (20/180)*100

=100/9

**Question. Prince sold a watch to deepak at 20% profit. Deepak sold it to Pushpendra at 25% profit. If Pushpendra paid 900rs , then Prince had purchased the watch ?**

**Solution:** Let Prince’s cost price=100

Prince selling price= 100*(100+20)/100

=120

Deepak’s cost price=120 rs

Deepak’s selling price=120*(100+25)/100

=150

Pushpendra’s cost price=150rs

If Pushpendra cost price is 150 , then Prince cost price=100 rs

Hence if Pushpendra’s cost price is rs 900, then Prince’s cost price

=(100/150)*900

=600 Rs

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