PROFIT AND LOSS, PARTNERSHIP
In our daily life and in the world of
business we continually encounter transactions involving sales and purchases.
Every time such a transaction occurs, it may be observed that there is a seller
and a buyer involved. The seller sells things/goods for a certain amount paid
by the buyer. The seller, eventually makes some profit or loss in the
transaction. This chapter deals with various aspects relating to such
transactions of sales and purchases. .
Cost Price (C.P) .
The price at which an article is purchased or
manufactured is called its cost price. .
Selling Price (S.P) .
The price at which an article is sold, is
called its selling price. .
If the selling price of an article is greater
than its cost price, we say that there is a profit (or) gain. .
Profit = selling price — cost price
Percentage of profit is always calculated on
the cost price of the article. .
When S.P. > C.P. .
(i) Profit = S.P. - C.P. .
(ii) S.P. = C.P. + Profit .
(iii) C.P. = S.P. - Profit .
(iv) Profit % = x 100
(v) Profit = Profit % x C.P. .
(vi) When C.P. and Profit % are given .
S.P. = C.P. x
S.P. and profit % are given .
If the selling price of an article is less
than its cost price, we say that there is a loss. .
Loss = Cost Price — Selling Price
Percentage of loss is always calculated on
the cost price of the article. .
When S.P. < C.P. .
(i) Loss = C.P. - S.P. .
(ii) S.P. = C.P. - Loss .
(iii) C.P. = S.P. + Loss .
(iv) Loss % = x 100
(v) Loss = Loss% x C.P. .
(vi) When C.P. and Loss % are given .
S.P. = C.P. x
(vii) When S.P. and Loss % are given .
All the expenditure incurred towards
transportation, repairs, etc (if any) are categorised as overheads. These
overheads are always included in the C.P. of the article. .
Note: When there are
two articles having the same cost price and if one article is sold at a% profit
and the other is sold at a% loss, then effectively neither profit nor loss is
made. If there are two articles having the same selling price and one is sold
at x% profit and the other is sold at x% loss, effectively, a loss will 2
always be made and the loss percent is%.
These days we know that competition is very
high in business. So in order to survive this competition and to boost the sale
of goods, the shopkeepers offer reJpates to the customers. The rebate offered
is called Discount. .
Discount is always calculated on the Marked
Price (M.P.) of the article. .
= M.P. — S. P. .
% = x 100
= M.P. - Discount .
= S.P. + Discount .
M.P and Discount % are given, .
S.P. and Discount % are given, .
(vii) If Profit is made,
C.P = M.P. - Discount -
(viii) If Loss is made,
C.P = M.P. - Discount + Loss
When a series of discounts are given we call
them Successive Discounts. .
Note: When an article
is sold after two Successive Discounts of p% and q%, then the final selling
Suppose an item is sold after successive
discounts of p%, q% and r% then its final selling price is given by
Marked price x
For example when two successive discounts of
10% and 20% are given, then the selling price
Let the M.P. be 100, S.P. = = 72
Effective Discount = M.P. - S.P. = 100 - 72 =
The combined value of the two discounts = 10
+ 20 = 30%
We observe that effective discount, 28% is
less than 30%
Note: The effective
discount obtained after successive discounts is always less than a discount
whose percentage equals the sum of the successive discount percentages offered
on an article. In other words, the effective discount due to successive
discounts of p%, q% and r% is always less than (p + q+ r)%. .
Worked out Examples
selling price of an article is Rs.81, loss is 10%, then the cost price is .
that S.P. = Rs.81 .
% of loss = 10%
Let C.P. be Rs.x .
\ Loss = (x - 81)
We have, % of loss = (100)
10 = 100
&⇒ x = 10x - 810
&⇒ 9x = 810
&⇒ x = 90
\ C.P = Rs.90 .
If an article is sold at 19% profit instead
of 12% profit, then the profit would be Rs.105 more. What is the cost price? .
cost price of an article be Rs.x. .
\ (19% of x) - (12% of x) = 105
&⇒ 7x = 105 x 100
&⇒ x = 1500
\ Cost Price = Rs.1500 .
If a trader sold two cars each at Rs.3520 and
gains 12% on the first and loses 12% on the second, then his profit or loss
percent on the whole is .
S.P. of each car is Rs.3520, he gains 12% on
the first car and loses 12% on the second car. .
In this case, effect will be loss and
percentage of loss is given by
= = 1.44%
A sold an article to B at 10% profit and B
sold it to C at 15% loss. If difference in the purchasing prices of A and C is Rs.58.5,
find the cost price of B. .
Let A purchased the article for Rs.100. Then
the C.Ps of B and C are Rs.110 and Rs.93.5 respectively. .
Let 6.5% be equal to 58.5. 110% will be equal
? = i.e. Rs.990.
The selling price of 12 articles is equal to
the cost price of 15 articles. Find the profit/loss percentage. .
cost price of each article be Rs.1. .
Cost price of 12 articles = Rs.12. .
Selling price of 12 articles = Cost price of
15 articles = Rs.15. .
Profit is made in selling 12 articles since
their selling price exceeds their cost price. Profit made in selling 12
articles = Rs.3. .
Profit percentage = 25%. .