# Formulas For Profit And Loss

## Formulas for Profit and Loss Questions

Important Formulas for Profit and Loss are given here on this page.

Profit (P)   The amount gained by selling a product for more than its cost price.

Loss (L) – The amount the seller incurs after selling the product less than its cost price is mentioned as a loss.

### Formulas for Profit and Loss

• Cost Price – It is basically the price at which a commodity or object is bought at. e.g. Shopkeeper buying Sugar from Farmer to sell in his grocery store. In its short form it is denoted as C.P.
• Selling Price – The price at which the commodity is sold at. e.g. Shopkeeper selling sugar to his customer. In its short form is denoted as S.P.
• Gain or Profit – If Cost Price is lesser than Selling Price, gain is made.
• Loss – If Cost price is greater than the Selling price, Loss is incurred.

### 1.  C.P in case of gain:

$\left (\frac{100}{100 + Gain} \right )\times S.P$

### 2.  C.P in case of Loss:

$\left (\frac{100}{100 – Loss} \right )\times S.P$

### 3. S.P in case of Gain:

$\left (\frac{100 + Gain}{100} \right )\times C.P$

### 4. S.P in case of Loss:

$\left (\frac{100 – Loss}{100} \right )\times C.P$

### Other Important Formulas for Profit and Loss

ProfitLoss
CP<SPCP>SP
Profit% = $\frac{profit}{\text{ Cost Price}}\times100$Loss% =$\frac{Loss}{\text{ Cost Price}}\times100$
Cost Price = $\frac{Profit}{\text{Profit Percentage}}\times 100$Loss =$\frac{\text{ Loss Percentage}}{100}\times$ Cost Price
Profit = $\frac{\text{ Profit Percentage}}{100}\times$ Cost PriceCost Price= $\frac{Loss}{\text{Loss Percentage}}\times$ 100

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### Some Important Formulas for Profit and Loss

• Profit = Selling Price – Cost Price
• Loss = Cost Price – Selling Price
• Profit % = (Profit / Cost Price) × 100%
• Loss% = (Loss / Cost Price) × 100%
• Selling Price = [(100 + Profit%)/100] × Cost Price
• Cost Price = [100/(100 + Profit%)] × Selling Price
• Selling Price = [(100 – Loss%)/100] × Cost Price
• Cost Price = [100/(100 – Loss%)] × Selling Price
• Discount = Marked Price – Selling Price

### Other Important Formulas

1. If you sell two items at same selling price “s” first at x% profit and 2nd one at x% loss. Then a loss is incurred always, which is given by

$( \frac{x}{10})^2$

2. Discount Percentage :

$\left ( \frac{Discount}{Marked \: Price} \right )\times 100$

3. Successive discounts:

If d1% , d2% d3%are successive discounts on marked price,
Selling price=marked price $\left ( \frac{100-d_{1}}{100}\right )\times \left ( \frac{100-d_{2}}{100}\right )\times \left ( \frac{100-d_{3}}{100}\right )$

Note:
(a) If there is no discount, the marked price is equal to the selling price
(b) Discount is always calculated on marked price unless otherwise stated.

### Question 1:

The small vegetable vendor bought some quantities of carrots and potatoes. If the cost price of 24 carrots is the same as the selling price number of a particular number of potatoes, then find the number of potatoes. (Given that the profit% is 50%)

1. 12
2. 16
3. 20
4. 24

### Solution:

Let’s say the required number of potatoes is p.

It is given that CP of 24 potatoes is same as the SP of p number of potatoes

So,  24(CP) = p(SP)

$\Rightarrow \frac{SP}{CP} = \frac{24}{p}$

Now, given profit% = 50%.

So, $\Rightarrow \frac{\text{(SP-CP)}}{CP} = \frac{50}{100} = \frac{1}{2}$

$\Rightarrow \frac{24-p}{p} = \frac{1}{2}$

$\Rightarrow p = 2 \times (24-p) = 48 – 2p$

$\Rightarrow 3p = 48$

$\Rightarrow p = 16$

### Question 2

If the selling price triples,  the new profit becomes six times the initial profit. Find the profit percentage.

1. 66%
2. 55.55%
3. 66.66%
4. 24%

### Solution:

Let the CP be Rs. x and SP be Rs. y.

According to the question, when selling price triples, the new profit becomes six times the initial profit.

Initial profit = y – x New profit = 6(y – x)

Therefore $\Rightarrow 6(y – x) = (3y – x)$

$\Rightarrow 6y – 6x = 3y – x$

$\Rightarrow 3y = 5x$

$\Rightarrow y = \frac{5x}{3}$

Soo, profit = y – x = $\frac{5x}{3} – x = \frac{2x}{3}$

Profit % = $\frac{\text{Profit}}{CP} \times 100$

= $\frac{\frac{2x}{3}}{x} \times 100$

= 66.66%

### Question 3

A shopkeeper mixes 10kg of pulses at Rs 5 per kg with 30 kg of pulses of another variety at Rs. 15 per kg. He then sells the mixed pulses at Rs. 20 per kg. How much is the profit or loss percentage?

1. 60% Profit
2. 60% Loss
3. 50% Profit
4. No profit no loss

### Solution:

Total amount of pulses = 10 kg + 30 kg = 40 kg.

CP of 40kg pulses = (10 *5) + (15 * 30) = Rs. 500

Rate at which he sells pulses = Rs. 20 per kg.

SP of 40kg pulses = 20 * 40 = Rs. 800

Therefore, the profit he makes = Rs. (800 – 500) = Rs. 300

Profit % = $\frac{300}{500} \times 100$ = 60% profit

### Question 4

During the end of the season sale, the owner of an apparel store decided to increase the price of clothes by 30%, and then introduced two successive discounts of 10% and 15%. What is the profit or loss percentage?

1. 5% loss
2. 6.33% loss
3. 5.3% profit
4. No profit no loss

### Solution:

Let the CP of one product be Rs. 100

A 30% increase in price means the selling price of that product = Rs. 130

10% discount on Rs. 130 = $\frac{130 \times 10}{100}$ = Rs. 13

So, the first selling price = (130 – 13) = Rs. 117

Now, 15% discount is applied to this new SP, = $\frac{117 \times 10}{100}$ = Rs. 11.7

So, the final SP = 117 – 11.7 = Rs. 105.3

The CP of the apparel was Rs. 100 and the final SP was Rs. 105.3. So, profit = Rs. 5.3

Therefore, the Profit% = $\frac{5.3}{100} \times 100$ = 5.3% profit

### Question 5

Assume you want to gift your friend his favorite novel for his birthday. The selling price of the novel at a bookstore is Rs. 600, including the taxes. The rate of tax is 10%. If the bookseller made a profit of 20%, then what is the cost price of the book?

1. 200
2. 400
3. 500
4. None of the above

### Solution:

As 10% is tax for the selling price of the book, we can say that 110% of SP = 600

So, SP = $\frac{600 \times 100}{110}$

Therefore, CP = $\frac{110 \times \frac{600 \times 100}{110}}{120}$

= Rs. 500.

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