** PROFIT AND LOSS**

SOME IMPORTANT SUTRAS

*. Profit = selling price – cost price

*. Loss = cost price – selling price

*. Cost price = selling price – profit

*. Cost price = selling price + loss

*. Selling price = cost price + profit

*. Selling price = cost price – loss

*. Profit percent = profit × 100/cost price

*. Loss percent = loss ×100/cost price

*. Cost price = SP ×100/(100+P)

*. Cost price = SP ×100/(100 – L)

*. Selling price = CP(100+P)/100

*. Selling price = CP(100-L)/100

*. If a dishonest sellsman sell his goods on CP but he uses fake weight instead of original weight , then the profit percent =

100(original weight – fake weight)/fake weight

*. If a dishonest sellsman use x% less weight, but he also sells his goods at y% profit/loss, then net percentage profit/loss = (+-y+x)100/100-x

*. If a sellsman wants to earn b% profit after selling his goods at a% discount , then the sufficient increment in the marked price of the goods is = 100(b+a)/100-a

*. If P sells a object to Q at a% profit/loss , and then Q sells that object to R at b% profit/loss , if R gives A rupees, then the cost price for P is =

100×100×A/(100+-a)(100+-b)

*. If a% and b% are two successive profit/loss on any object then the resultant profit/loss =

(+-)a + (+-)b + [(+-)a(+-)b/100]

*. A sellsman sells his goods at a% profit , if he sells his goods at R rupees more, then he earn b% profit , then cost price of goods is = 100×R/(b-a)

*. A object is sells at a% profit, if CP and SP both are less by rupees R , then he earn b% more profit, then the CP of the object is = R(a+b)/b

*. If CP of (a) objects is equal to the SP of (b) objects , then the profit percent = 100(a-b)/b

*. If a part of a object is sells at x% profit/loss , b parts at y% profit/loss and c parts at z% profit/loss, this makes total profit/loss of R rupees, then the CP of the objects is =

100×R/(ax+by+cz)

*. If A th part of any object is sells with x% loss, if further there will be no loss or profit in whole transaction, for this, the profit percent for the remaining parts of the object should be =

Ax/(1-A)%

*. The selling price of two objects is Rs X , if one object is sold at r% loss and other object is sold at R% profit- then

**. The CP of the object which are sold at profit =

x(100+R)/(200-r+R)

**. CP at loss = x(100-r)/(200-r+R)

*. If a object is sold at Rs A with r% profit/loss, then the selling price of the object, if it is sold with R% profit/loss is = A(100+-R)/(100+-r)

*. If a person sold a object with R% profit/loss instead of r% profit/loss and gains the profit of Rs A, then the CP of the object = 100A/R-r

*. If the selling price of two objects are same, one object sold at r% profit and other object sold at r% loss, in this type of transaction always occurred loss, then the loss percent is = r^2/100

*. If CP of x objects is equal to the SP of y objects, if x>y then always be profit then profit percent = 100(x-y)/y , but if x<y then always be loss, then loss percent = 100(y-x)/y

*. A buys a object in Rs x, and sells it to B at r% profit/loss, again B sells it to A at R% profit/loss , then profit of A in this transaction =

x(100+-r/100)(1-[100+-R/100])

*. r% profit/loss been if x objects are bought in 1 rupees , then the numbers of objects selling in 1 rupees will be = 1×100/100+-r

*. A person buy y objects in x rupees, and then he sells x objects in y rupees-

If x>y then loss percent = (x^2 – y^2)100/x^2

If x<y , then profit percent = (y^2 – x^2)100/x^2

*. A person sells a object in x% profit/loss , if he bought at y% less/more, and sell at Rs A more/less , then he gains the profit of z% then the CP of the object =

A[(100+-y/100)(100+-z/100) – (100+-x/100)]

*. After selling a object in x rupees, the gained profit/loss is equal to the cost price of that object then the cost price is = +-50+-10√(25+-x)

*. If a object is bought at the rate of (a) in x rupees, and sells at the rate of (b) in y rupees-then the percentage profit = (ay-bx)100/bx

*. A sellsman cheat while buying object with x% and while selling object he again cheat with x% , then the profit percent = 2x + x^2/100

*. A object with having CP of x rupees, is sold with y% profit , and by another person that object is sold again with z% profit/loss , then the final selling price of that object will be =

x(100+-y/100)(100+-z/100)

*. A shopkeeper sells his object at cost price with a% profit/loss , but he use b grams instead of c grams , then profit/loss percent =

[(c/a)(100+-a) – 100]%

*. The decrease/increases in the usage of the object such that expenditure only increase/decrease by y%, if x% gets increases/decrease in the value of the object is =

[1 – (100+-y/100+-x)]100%

*. After selling a object in x rupees , the gained profit is equal to the loss obtained while selling the object in y rupees, then the CP of the object is = x+y/2