Quantitative Aptitude Profit and Loss Study Material
A consumer goes to the market and buys certain goods. The buyer is called a customer and the shopkeeper who sells the goods to him is called a retailer. The retailer in turn purchases goods in bulk from a wholesaler who keeps a largo stock of goods. In the retailer-wholesaler deal, the retailer becomes the customer.
Cost Price (C.P.): The price at which a person buys an article is called the Cost Price (C.P.) of the article.
Selling Price (S.P.): The price at which an article is sold “is called the Selling Price (SP) of the article. Whenever there is a transaction between the two parties i.e.the buyer and the seller, the price at which the article is sold by the seller is same as the price at which it is purchased by the buyer. Normally, the Cost iPrice and the Selling Price in a problem are commonly used in a slightly modified sense. This is clarified by the following illustration.
A sells an article to B at price Rs.x, B in turn sells it to C at price Rs. y. Here, Rs. x is the Selling Price for A as well as the Cost Price for B. But the Selling Price for B is Rs. y which is also the, Cost Price for C.
Profit or Gain : Whenever a person sells an article at price greater than the Cost Price he is said to have made a profit or gain.
Profit or Gain = SP-CP.
• In the above example B’s profit= Rs. y – Rs. x
Loss: When S.P. is less than the C.P., one makes a loss. Loss = C.P.-S.P.
In the above example B’s loss= Rs. x – Rs. y.
Note: S.P. and C.P. must be for the same article and for the same quantity and also must be referred to the same person while calculating profit or loss. . .
For example, we can’t take the difference of the Price of table and chair; or difference of Cost Price of 10 kg’s of Sugar and Selling Price of 2 kgs of Sugar for calculating profit or loss. Further, if we are calculating B’s profit or loss, then B’s C.P. and S.P. should be used and not A’s or C’s.
Note: Profit or Loss are always reckoned on Cost Price Gain per cent or % gain is gain on the reference value & Rs. 100.
Loss per cent or % loss is loss on the reference value & Rs. 100.
Some important formula
Gain = S.P.-CP. .
Loss = C.P.-S.P.
Overheads : The expenses incurred on transportation, rent, personnel salary, maintenance, packaging, advertise-ments and the like are included under the general heading of Overheads. These .overheads and the profit when added to the cost price determine the Selling Price. If the overheads are not separately mentioned in the problem, we assume it to be zero or else they have been included in the Cost Price itself.
Discount: It is an offer made by the seller to the buyer for reduction in price to be paid. There are several cases where discounts are allowed. For instance, to dispose off old goods, to increase its market share, when the cus¬tomer is ready to pay the whole amount in cash instead of payments in instalments and so on. It is subtracted from the original price and is usually expressed as per cent or a fraction of the market price. The price obtained after deducting the discount from the original price is the selling price which the customer has to pay.
We will now discuss various cases on profit and loss through general derivations for special cases and problem-solving.
Ex. Ram buys a pen for Rs. 12 and sells it for Rs. 15. Find his gain per cent.
From the general rule we can easily write the basic formulae using proper signs.
You can notice that % profit is analogous to% increase and % loss is analogous to % decrease.
Ex.. A man buys 9 pens for Rs. 90 and sells 8 pens for Rs. 88. How much profit or loss does he make ?
Sol. We will solve this problem in two ways and later on using the direct expression too after we derive it in the next example.
Method I: S.P. of 8 pens is Rs. 88.
S.P of 1 pen is 88/8 =11
S.P. of 9 pens = 11 x 9 = Rs. 99 or 88/8x 9 = Rs. 99.
C.P of 9 pens is 90
Profit = Rs 99-Rs 90 = Rs 9
Note: We didn’t calculate the C.P. of 8 pens (which would be Rs. 80) and subtract it from S.P. of 8 pens (which is Rs. 88) to get a profit of (88 – 80) = Rs. 8 because the person has already bought 9 pens by investing Rs. 90. And we always calculate profit or loss on investment (which is related to C.P. and not to S.P.). However, for % profit or loss we can choose any common quantity for C.P. and S.P. For example, here we take either 9 or 8 pens conveniently.
For 8 pens, % profit = 88-80/80 x 100% = 10%
For 9 pens, % profit = 99-90/90x 100% = 10% ‘
We can see that we get the same result in both the cases.
Method II: Applicable when profit or loss is to be determined in per cent terms and not when net profit or loss amount is to be determined.
Take the LCM of quantities bought and sold.
Find C.P. and S.P. for the LCM quantity. Calculate % profit or loss. .
LCM of 9 and 8 is 72.
C.P. of 72 pens 72/9 x 90 = 720
S.P. of 72 pens 72/8 x 88 = 792
% profit = 792-720/720 x 100% = 72/720 x 100%
% profit = 10 %
General rule for finding C.P/S.P when percent Profit/loss is given
Formula Short cut for conclusion