Important Formulas (Part 1) - Profit and Loss 1. Cost price and selling price

Cost price (CP) is the price at which an article is purchased.

Selling price (SP) is the price at which an article is sold.

2. Profit and loss

If selling price is more than cost price, profit(gain) occurs.

If selling price is less than cost price, loss occurs.

In case of profit,
profit = selling price – cost price

selling price = cost price + profit

cost price = selling price - profit

In case of loss,
loss = cost price - selling price

selling price = cost price - loss

cost price = selling price + loss
3. Profit percentage and loss percentage

Profit percentage and loss percentage are always calculated on cost price unless otherwise stated.

In case of profit,
$\text{profit percentage}=\dfrac{\text{profit}×100}{\text{cost price}}$

$\text{selling price}\\=\text{cost price}+\dfrac{\text{cost price}×\text{profit percentage}}{100}\\ \\=\dfrac{\text{cost price}(100+\text{profit percentage})}{100}$

$\text{cost price}=\dfrac{100×\text{selling price}}{100+\text{profit percentage}}$

Example: If an object is sold at a profit of $20\%,$
selling price $=120\%$ of cost price

In case of loss,
$\text{loss percentage}=\dfrac{\text{loss}×100}{\text{cost price}}$

$\text{selling price}\\=\text{cost price}-\dfrac{\text{cost price}×\text{loss percentage}}{100}\\=\dfrac{\text{cost price}(100-\text{loss percentage})}{100}$

$\text{cost price}=\dfrac{100×\text{selling price}}{100-\text{loss percentage}}$

Example: If an object is sold at a loss of $20\%$
selling price $=80\%$ of cost price

4. Selling at same price
(4.1) Suppose a person sells two objects at the same price, one at a profit of $x_1\%$ and another at a profit of $x_2\%.$ Then,
net profit percentage $=\dfrac{100(x_1+x_2)+2x_1x_2}{200+x_1+x_2}$
Note:
(a) for loss, use -sign for $x_1$ and/or $x_2$ as applicable.
(b) If the formula evaluates to a -ve value, it means there is a net loss

Example 1: Two objects are sold at the same price, one at a profit of $10\%$ and another at a profit of $32\%$. Then,
$\dfrac{100(10+32)+2×10×32}{200+10+32}=20\%$
i.e., there is a net profit percentage of $20\%$

Example 2: Two objects are sold at the same price, one at a profit of $40\%$ and another at a loss of $16\%$. Then,
$\dfrac{100(40-16)+2×40×(-16)}{200+40-16}=5\%$
i.e., there is a net profit percentage of $5\%$

Example 3: Two objects are sold at the same price, one at a profit of $20\%$ and another at a loss of $28\%$. Then,
$\dfrac{100(20-28)+2×20×(-28)}{200+20-28}=-10\%$
i.e., there is a net loss percentage of $10\%$

Example 4: Two objects are sold at the same price, one at a loss of $10\%$ and another at a loss of $28\%$. Then,
$\dfrac{100(-10-28)+2×(-10)×(-28)}{200-10-28}=-20\%$
i.e., there is a net loss percentage of $20\%$

(4.2) Suppose a trader sells two objects at the same price, one at a profit of $x\%$ and another at a loss of $x\%.$ Then he always incurs a net loss expressed as
net loss percentage $=\left(\dfrac{x}{10}\right)^2$

Example: Two objects are sold at the same price, one at a loss of $22\%$ and another at a loss of $22\%$. Then,
net loss percentage $=\left(\dfrac{22}{10}\right)^2=4.84\%$

Rohan G
2016-08-12 16:23:46
In rule/formula no.15, if % loss and % gain are not same, then what will be the formula? Or how to solve these kind of problems.?
jiju (Junior Maths Expert, careerbless.com)
2016-08-12 20:40:17
see the formula and derivation: Q.684

Aaryan
2015-10-02 15:09:19
Can someone please explain rule/formula no. 15?
sameer
2016-01-11 21:53:44
Let the S.P is 500 both item
For 10%loss= C.P is 555.55
For 10%profit=C.P is 454.5

Therefore
total s.p of 2 items=1000
total c.p of 2 items=1010.05
Therefore overall loss can b calculated by above formula
Vikram
2015-10-30 03:52:04
If two articles sold at the same price, one is at 12% profit and other is at 12% loss, then the seller always incurs a loss expressed as:

Loss% = (12/10)^2 = (144/100) =1.44%
Pritham
2015-10-18 02:04:58
They said a trader sold two goods at same price ,say 100 rupees. After he sold both goods, one good got some loss which is equal to the profit of the other good,say 10%.

As the loss and profit percent are equal the trader will always get loss.Therefore,

Loss%=[(Common profit or loss percentage)/10]2
Jay
2015-10-03 02:02:19
See Q.19 in Solved Examples
swapnil
2015-04-01 07:37:21
Guys else tell me the formulas of selling price,how to find cost price of one item & total profit
Ranjith
2015-03-12 17:25:21
By selling 15 dozen Bananas, a fruit seller lost an amount equal to the selling price of 20 bananas, find the loss percentage
2015-08-17 11:12:00
let the S.P of each banana be 1, then S.P of 180 bananas is 180
loss = S.P of 20 bananas = 20

we know loss = C.P - S.P , then C.P = S.P + loss
so CP of 180 bananas = 180 + 20 = 200
Loss percent = $\dfrac{\text{Loss}}{\text{CP}}×100=\dfrac{20}{200}×100$

after cutting it we will find the answer is 10% loss
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