Profit loss and discount is one of the most important and frequently tested topics in quantitative aptitude. It is asked in almost every competitive exam including CAT, SSC CGL, SSC CHSL, Bank PO, Bank Clerk, Railway RRB and CSAT. A strong understanding of profit loss and discount concept, formulas and tricks is essential for scoring well in these exams. In this post we cover everything from the basic definition of cost price, selling price, profit and loss percentage formulas, overall loss formula when two articles are sold at same selling price, marked price and discount concept, selling price formula, and banker’s discount including true discount and banker’s gain — all explained with clear formulas and solved examples.
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 = \(\frac{{S.I. \times T.D.}}{{S.I. – T.D.}}\)