Profit Loss and Discount
Cost Price (CP):- The price at which the article is bought.
Selling Price(SP):- The price at which the article is sold
Profit or gain:-
profit or gain = SP – CP
% Profit = \(\frac{{SP – CP}}{{CP}}\)×100%
Loss:- When CP is greater than SP
Loss = CP – SP
% Loss = \(\frac{{CP – SP}}{{CP}}\)×100%
● profit or Loss is always calculated on the basis of cost price unless otherwise mentioned in the problem.
● while solving questions we compare actual value with the ratio value to find out the required value of answer.
Ex:- If CP = 200 Profit = 40% SP = ?
∴ SP = 200 + 80 = 280
Ex:- If \(6\frac{1}{4}\)% profit fetches a profit of Rs. 75 on an article then find the cost price of the article.
Sol:
Ex:- If 30% Loss on selling an article makes the trader to suffer a loss of Rs. 90 then find the selling price of the article.
Sol:-
Ex:- By selling an article for Rs. 500, a man loses 25%. At what price will he sell in order to gain 25% ?
Sol:-
● When two different articles sold at same selling price and when % gain on first article = % Loss on second article = x%
So, always there is overall loss in the transaction.
overall % Loss = -\({\left( {\frac{x}{{100}}} \right)^2}\) = – \(\frac{{{x^2}}}{{100}}\)%
Ex:- Two mobiles were sold for 12500 Rs. each. On one a gain of 25% is made and on other, a loss of 25% is made. How much % loss or gain is made in the whole transaction ?
Sol:- overall % loss = – \(\frac{{{{25}^2}}}{{100}}\) = – 6.25% Answer
Discount and Marked Price(MP):-
Selling Price (SP) = MP(1 – %discount)
● Discount = MP – SP
\(\% D = \frac{D}{{MP}} \times 100\)
So Discount is given on marked price.
●
(i). Banker’s discount (B.D.) = \(\frac{{Bill\;amount \times rate \times time}}{{100}}\)
(ii). Banker’s gain (B.G.) = Banker’s discount (B.D.) – True Discount (T.D.) = \(\frac{{{{(T.D.)}^2}}}{{\Pr esent\;Worth\;(P.W.)}}\)
(iii). Ture discount (T.D.) = \(\frac{{B.D. \times 100}}{{100 + rate \times time}} = \frac{{bill\;amount \times rate \times time}}{{100 + rate \times time}} = \sqrt {P.W. \times B.G.} = \frac{{B.G. \times 100}}{{rate \times time}}\)
(iv). Present worth = Bill amount – Ture discount
(V). Sum = \(\frac{{S.I. \times T.D.}}{{S.I. – T.D.}}\)