__PROFIT & LOSS__Profit and loss are determined by the value of cost price and selling price. Cost price is the price at which an article is purchased and selling price is the price at which article is sold

**Profit = selling price - Cost price **
**Loss = Cost price - Selling price **

**Percentage profit and loss are always calculated on cost price. **
**☞**If a cost price of m articles is equal to the selling Price of n articles, then Profit percentage

__MARKED PRICE__Marked price is also known as the list price. It is the price which is marked on the article.

Where CP = cost price and MP = marked price

__DISCOUNT__Shopkeepers devise several ways to attract customers (consumers). Sometimes they sell an article at a price lower than its list price (LP)/marked price (MP). Recall that reduction offered by retailer on the list price is called discount. We may recall that

Discount = MP - SP

**Example 1: Marked price of a dining table is Rs 1350. It is sold at Rs. 1188 after allowing certain discount. Find the rate of discount.**

**Solution:**MP of the dining table = Rs. 1350

SP of the dining table = Rs. 1188

Discount allowed = Rs. (1350 - 1188) = Rs. 162

Discount percent =162/1350×100=12

This the rate of discount is 12%

As we had discussed the Multiplying Factor concept, it is very helpful to calculate the S.P. and C.P.

**S.P. = C.P. × M.F.**In case of profit M.F. is greater then 1. If there is 10% profit, then

S.P. = C.P. × 1.1

M.F. = 1.1

For 15% profit M.F. = 1.5

**Let’s take an example**If markup percentage is 30%, and the profit percentage is 17% then find the discount percentage.

Let

CP = 100

M.P. = 100 × 1.3 = 130

(M.P. – Marked up price)

S.P. = 100 × 1.17 = 117

**Discount %**M.P. × Multiplying factor = S.P

130 × M.F. = 117

M.F = .9

Discount Percentage = 10%

**In case of Loss S.P < C.P ****And M.F. is smaller then 1.****Relation between multiplying factor of, Profit, Mark-up and discount****MF profit = MF mark-up × MF discount.**

__SUCCESSIVE DISCOUNTS__Sometimes more than one discount are offered by the shopkeeper on a single item or article. When two or more discounts are applicable successively to the list price of an article, they form the discount series.

Suppose a shopkeeper is offering 3 successive discounts of 10%, 20% and 30% then to calculate effective discount we assume that marked price is 100, then final value becomes 0.90 × 0.80 × 0.70 × 100 = 0.54 × 100 = 50.4

Total discount = 49.6%.

**☞**When there are two successive Profit of x % and y % then the resultant profit per cent is given by

**☞**If there is a Profit of x% and loss of y % in a transaction, then the resultant profit or loss% is given by

**Note-** For profit use sign + in previous formula and for loss use – sign.

if resultant come + then there will be overall profit, if it come – then there will be overall loss.

**Example 2:****If two articles are sold at same selling price one at 30% profit another at 30% loss then what is his overall percentage profit or loss?**
__FALSE WEIGHT PROBLEMS__Shown or indicate weight is always equivalent to selling price, and actual/true weight is equivalent to cost price.

**☞**If a trader professes to sell his goods at cost price, but uses false weights, then

**Example 3:****A shopkeeper takes 20%, extra quantity while purchasing the milk, and gives 25% less than the indicated weight while selling the milk. Find the profit percentage of he sells at the cost price only. ****Solution: **Suppose the price of milk = 1 Rs per ml shopkeeper takes 120 ml, and pays only Rs. 100

While selling he gives only 75 ml and shows 100 ml.

Total selling price of 120 ml

100/75×120 = 160, hence percentage profit = 60%