Profit-Loss-Part-2
Profit-Loss-Part-2

Profit & Loss for all competitive exams with Tricks

Profit & Loss for all competitive exams with Tricks

Profit and loss are the terms related to monetary of transactions in trade and business. Therefore, Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is.

The important terms covered here are cost price, fixed, variable and semi-variable cost, selling price, marked price, list price, margin, etc.

Profit(P)

The amount gained by selling a product with 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.
Cost Price (CP)

This is the price at which an article is purchased or manufactured.

Selling Price (SP)

This is the price at which an article is sold.

Fixed Cost: 

The fixed cost is constant, it doesn’t vary under any circumstances

Variable Cost: 

It could vary depending as per the number of units

Marked Price Formula (MP)

This is basically labelled by shopkeepers to offer a discount to the customers in such a way that,

Overhead Charges Such charges are the extra expenditures on purchased goods apart from actual cost price. For example, charges, rent, salary of employees, repairing cost on purchased articles etc.

Basic formula of profit and loss

Profit, P = SP – CP; SP>CP

Loss, L = CP – SP; CP>SP

P% = (P/CP) x 100

L% = (L/CP) x 100

SP = {(100 + P%)/100} x CP

SP = {(100 – L%)/100} x CP

CP = {100/(100 + P%)} x SP

CP = {100/(100 – L%)} x SP

Profit and Loss Examples

If a salesperson has bought a textile material for Rs.300 and he has to sell it for Rs.250/-, then he has gone through a loss of Rs.50/-.

Suppose, Ram brings a football for Rs. 500/- and he sells it to his friend for Rs. 600/-, then Ram has made a profit of Rs.100 with the gain percentage of 20%.

Ex: For the above example calculate the percentage of the profit gained by the shopkeeper.

Solution:

We know, Profit percentage = (Profit /Cost Price) x 100

Therefore, Profit percentage = (20/100) x 100 = 20%.

Ex: Suppose a shopkeeper has bought 1 kg of apples for 100 rs. And sold it for Rs. 120 per kg. How much is the profit gained by him?

Solution:

Cost Price for apples is 100 rs.

Selling Price for apples is 120 rs.

Then profit gained by shopkeeper is ; P = SP – CP

P = 120 – 100 = Rs. 20/-

Trick-1

If a person sells two similar articles, one at a gain of a% and another at a loss of a%, then the seller always incurs a loss which is given by

Loss\% =\ (a/10)^2\%

Note In this case, SP is immaterial

Ex. A man sold two radios for Rs.2000 each. On one he gains 16% and on the other he losses 16%. Find his gain or loss per cent in the whole transaction.

Here a=16% As per formula

Loss\% =\ (a/10)^2\%\\
Loss\% =\ (16/10)^2\%\\
=\ (256/100)\%\\
=2.56\%

Trick-2

If ‘a’ th part of some items is sold at x% loss, then required gain per cent in selling rest of the items in order that there is neither gain nor loss in

Whole\ Transection\ is = \left(\frac{ax}{1-a}\right)\%

Ex. A medical store owner purchased medicines worth Rs. 6000 from a company. He sold 1/3 part of the medicine at 30% loss. On which gain he should sell his rest of the medicines, so that he has neither gain nor loss?

Sol. As given a = 1/3 and x = 30% Therefore, required gain %

required\ gain\ percent\ is = \left(\frac{ax}{1-a}\right)\% \\ =\left(\frac{1/3\times30}{1-1/3}\right)\% \\ 
 \\ =\left(\frac{10\times3}{2}\right)\% \\ =\left(\frac{30}{2}\right)\% \\ = \ 15 \%

Trick -3

A businessman sells his items at a profit/Loss of a%. If he had sold it for Rs. R more, he would have gained/lost b%. Then,

CP = \frac{R}{b\pm a}\ \times100

‘-‘ = when both are either profit or loss ‘+’ = When one is profit and other is loss.

TricK-4

If cost price of ‘a’ articles is equal to the selling price of ‘b’ articles, then

Profit\ Percentage = \frac{a-b}{b}\times100\%

Ex. If the cost price of 20 articles is equal to the selling price of 18 articles, then find the profit per cent.

Here a = 20, b = 18

Therefore,

Profit\ Percentage = \frac{a-b}{b}\times100\% \\ 
                               = \frac{20-18}{18}\times100\% \\=\frac{100}{9}\% 

Trick-5

Trick-5 If a man purchases m items for Rs x and sells n items for Rs y then Profit or Loss per cent is given by

= \frac{my-nx}{nx}\ \times100 \%

[positive result means and negative result means loss]

Ex. If Karan purchases 10 oranges for Rs. 25 and sells 9 oranges for Rs. 25, then find the gain percentage.

Here m = 10,  x= 25

And n = 9, y= 25

=\frac{10\times25-9\times25}{9\times25}\times100\%  =\frac{250-225}{225}\ \times100\% = \frac{25}{225}\times100\%=\frac{100}{9}\%

Trick-6

If A sold an article to B at a profit (loss) of r1 % and B sold this article to C at a profit (loss) of

r2 %, then cost price of article for C is given by

Cost\ Price\ for\ A\times\left(1\pm\frac{r_1}{100}\right)\left(1\pm\frac{r_2}{100}\right)

[Positive for profit and negative for loss is used.]

Ex. Nikunj sold a machine to Sonia at a profit of 30%. Sonia sold this machine to Anu at a loss of 20%. If Nikunj paid Rs. 5000 for this machine, then find the cost price of machine for Anu.

Trick-7

If a dishonest trader professes to sell his items at CP but uses false weight, then

Gain\% = \frac{Error}{True\ value-Error}\times100\% \\
or\\
Gain\% = \frac{True\ weight-False\ weight\ }{False\ weight}\times100\%

Here, while calculating gain or profit per cent, we have taken false weight as a base. Because CP is what is paid when an item is purchased or manufactured. Here, in this case dishonest trader is telling false weight to be the CP and he is gaining only when sells at false weight.

Ex. A dishonest dealer professes to sell his goods at cost price but he uses a weight of 930 g for 1 kg weight. Find his gain per cent.

Gain\% = \frac{1000-930\ }{930}\times100\%  = \frac{70\ }{930}\times100\%=\frac{700}{930}\%

Trick-8

If a shopkeeper sells his goods at a% loss on cost price but uses b g instead of c g, then his percentage profit or loss is

\left[\left(100-a\right)\frac{c}{b}-100\right]\%\ as\ sign\ positive\ or\ negative.

Ex. A dealer sells goods at 6% loss on cost price but uses 14 g instead of 16 g. What is his percentage profit or loss?

\left[\left(100-6\right)\frac{16}{14}-100\right]\%=[94\times\frac{16}{14}-100]\%

Trick-9

If a dealer sells his goods at a% profit or loss on cost price and uses b% less weight, then his percentage profit or loss will be

\frac{\left(b\pm a\right)}{100-b}\times100\%

+ sign used for profit, – Sign used for loss

Ex. A dealer sells his goods at 20% loss on cost price but uses 40% less weight. What is his percentage profit or loss?

Here a = 20% and b = 40% Required answer

\frac{\left(40-20\right)}{100-40}\times100\% =\frac{20}{60}\times100\%=\frac{100}{3}\%

Trick-10

If ‘a’ part of an article is sold at x% profit/loss, ‘b’ part at y% profit/loss and ‘c’ part at z% profit/loss and finally there is a profit/loss of Rs. R , then

Cost price of entire article

Rs.\frac{R\times100}{ax+by+cz}

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