## PROFIT AND LOSS

### Introduction

Cost Price = cost of item
Selling price = price at which item is sold.
Gain = Selling price – Cost price (SP > CP)
Loss = Cost price – Selling price (CP > SP)

 SP={(100+GAIN%) /100}*CP SP={(100-LOSS%)/100}*CP CP=100/(100+GAIN%)}*SP CP=100/(100-LOSS%)}*SP

So when an article of Rs 100 is sold at 35% gain that means SP is Rs.135
So when an article of CP = 100 is sold for loss of 35% its SP is Rs. 65.

When a item is sold for x% gain and other for x% loss, the seller incurs a loss of

 Loss = ( X / 10) ^ 2
• Direct Costs or Variable Costs : This is the cost associated with direct selling of product/service. In other words, this is the cost that varies with every unit of the product sold. Hence, if the variable cost in selling a pen for  20 is  5, then the variable cost for selling 10 units of the same pen is 10 × 5 = Rs. 50.

• Indirect Costs (Overhead Costs) or Fixed Costs : There are some types of costs that have to be incurred irrespective of the number of items sold and are called as fixed or indirect costs. For example, irrespective of the number of units of a product sold, the rent of the corporate office is fixed. Now, whether the company sells 10 units or 100 units, this rent is fixed and is hence a fixed cost.

• Apportionment of indirect (or fixed) costs : Fixed Costs are apportioned equally among each unit of the product sold. Thus, if n units of a product is sold, then the fixed cost to be apportioned to each unit sold is given by : Fixed costn

• The Concept of the Break-even Point : The break-even point is defined as the volume of sale at which there is no profit or no loss. In other words, the sales value in terms of the number of units sold at which the company breaks even is called the break-even point. This point is also called the break-even sales.

• Since for every unit of the product the contribution goes towards recovering the fixed costs, as soon as a company sells more than the break-even sales, the company starts earning a profit. Conversely, when the sales value in terms of the number of units is below the break-even sales, the company makes losses. The entire scenario is best described through the following example.

Q. Let us suppose that a paan shop has to pay a rent of  1000 per month and salaries of  4000 to the assistants. Also suppose that this paan shop sells only one variety of paan for  5 each

• The direct cost (variable cost) in making one paan is  2.50 per paan, then the margin is  (5 – 2.50) =  2.50 per paan.

• Now, break-even sales will be given by: Break-even-sales = Fixed costs/Margin per unit = 5000/2.5 = 2000 paans

• Hence, the paan shop breaks-even on a monthly basis by selling 2000 paans

• Selling every additional paan after the 2000th paan goes towards increasing the profit of the shop. Also, in the case of the shop incurring a loss, the number of paans that are left to be sold to break-even will determine the quantum of the loss

• Profit = (Actual sales – Break-even sales) × Contribution per unit

• Loss = (Break-even sales – Actual sales) × Contribution per unit

• Profit Calculation on the Basis of Equating the Amount Spent and the Amount Earned

• A fruit vendor recovers the cost of 25 mangoes by selling 20 mangoes. Find his percentage profit.

• Since the money spent is equal to the money earned the percentage profit is given by

• % Profit = Goods leftGoods sold100 = 5* 100/20 = 25%

IF THE TRADER PROFESSES TO SELL HIS GOODS AT COST PRICE BUT USES FALSE WEIGHTS,THEN

• GAIN= ERROR(TRUE VALUE)-(ERROR)100%

Q. A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 gms for a kg weight . Find his gain percent.

• GAIN= ERROR(TRUE VALUE)-(ERROR)100%

• 40960100%

• 4 1/6 %

Q. A person incurs loss of 5% by selling a watch for Rs 1140. At what price should the watch be sold to earn a  5% profit ?

A. CP is 100/95 * 1140 as a loss of 5% on CP is 1140 so CP is 100/95% of 1140 [SP] as per formula above.New selling price = (100 / 95) * ( 105 / 100) * 1140 = 1260

Q. By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .

A.

Selling price of 33m – CP of 33 m = SP of 11m [Gain].

SP of 22 m = CP of 33m i.e. SP of 2 m = CP of 3 m

Assume CP of 1 m = Re. 1 so 3 m is Rs. 3.

SP of 2 m = Rs. 3 and SP of 1 m = Rs. 1.5 so gain is 50%.

Q. A man brought toffees at 3 for a rupee. How many for a rupee must he sell to gain 50%?

A. Cost of a toffee is 3 toffees is re. 1. So he needs to sell them at Rs. 1.5 to make a gain of 50% so at 50 paise each or 2 for a rupee.

Q. A  grocer  purchased  80  kg  of  sugar  at Rs.13.50  per  kg  and mixed  it with 120kg sugar at Rs.16per kg. At what rate should he sell the mixer to gain 16%?

A. The cost of the mixture

= (weight1 * price1) + (weight2*price2) / (weight1+weight2)

= (80*13.5) + (120*16) / (120+80)

=(1080+1920)/200 = 3000/200 = Rs. 15 / kg

SP = 116/100 * 15 = 1.16*15=17.4 Rs

Q. Pure ghee cost Rs.100 per kg. After adulterating it with vegetable oil costing Rs.50 per kg,   A  shopkeeper  sells  the mixture at  the rate of Rs.96 per kg,  thereby making a profit of 20%. In What ratio does he mix the two?

A. SP of mixture = 96 ; CP of mixture = 80 as SP is 20% more than CP;

Rule of alligation:

(Quantity of oil : Quantity of ghee)

= ( CP of ghee – Mean price) / (Mean price – CP of oil)

= (100-80) / (80-50)

=20/30 = 2:3

Q. Monika purchased a pressure cooker at 9/10th of its selling price and sold it at 8% more than its S.P .find her gain percent.

A. Assume it was with a SP of Rs. 100 it was bought for Rs. 90 and sold for Rs. 108 thus making profit of Rs. 18 which is 20% more than Rs. 90.

Q. A  tradesman  sold  an  article  at  a  loss  of  20%. if  the  selling  price  has  been increased by Rs 100, there would have been a gain of 5%. what was the cost price of the article?

A. SP(old) = 80% of CP

SP(new) = 105% of CP; we know (105% of CP) – (80% of CP) = 100

i.e. 25% of CP = 100; Hence CP = Rs. 400

Q. A man sells an article at a profit of 25% if he had bought it 20% less and sold it for  Rs 10.50 less, he would have gained 30% find the cost price of the article.

A. SP1 = 1.25CP1 as it is sold for 25% profit. CP2 = (4/5)*CP1;

SP2 = (130/100)*CP2

SP2 = SP1 – 10.5 = 1.25CP1 – 10.5

so we get

1.25CP1 – 10.5 = (130/100)*(4/5)*CP1

1.25CP1 – 1.04CP1 = 10.5

0.21CP1 = 10.5

CP1 = Rs.50

Q. A dealer sold three-fourth of his article at a gain of 20% and remaining at a cost price. Find the gain earned by him at the two transaction.

A. assume he had 4 articles of CP = 100 so he sold three at 120 and 1 at 100. so he earned profit of Rs. 60. CP of total inventory is 400 so profit is 15%.

Q. A man bought a horse and a bull for Rs 3000.he sold the horse at a gain of 20% and the bull at a  loss of 10%,thereby gaining 2% on the whole. find the cost of the horse.

A. 1.2x + 0.9(3000-x) = 3600 is the equation as ‘x’ is price of horse. 1.2x is SP of horse at 20% profit and 0.9(3000-x) is SP of bull at 10% loss. rs 3600 is the SP of total transaction at 2% profit over Rs. 3000.

Q. find the single discount equivalent to a series discount of 20% ,10% and 5%

A. assume CP=100 so apply 20% discount to get CP=80 and then 10% to get 72 and then 5% to get 72-3.6 = 68.4 so total is 31.6%.

Q. A retailer marks all  its goods at 50% above  the cost price and thinking  that he will still make 25% profit,offers a discount of 25% on  the marked price.what is the actual profit on the sales?

A. Assume price is 100 so SP is 150 and 25% discount on SP gives new SP as Rs 112.5. So profit is 12.5%

Q. At what %  above C.P must  an  article be marked  so  as  to  gain  33%  after allowing a customer a discount of 5%?

A. We have to find the value of SP [assume as ‘x’] whose 95% is 33% above CP. Assume CP to be Rs 100 and SP(new) will be Rs. 133.

0.95x = 133

x = 133 * 100 / 95 = 133 * 20 / 19 = 140

Q. A merchant sold his goods for Rs.75 at a profit percent equal to C.P. The C.P was :

A. SP = (100+Gain%) * CP /100 we get below equation by substituting these values

75 = ( 100 + x) * x / 100

### Quiz

Score more than 80% marks and move ahead else stay back and read again!

Q1: Find selling price if gain of 20% is made on a good worth Rs. 300
360
330
300
350

ANS.360

Q2: Find selling price if loss of 20% is made on a good worth Rs. 300
240
250
260
270

ANS.240

Q3: Find cost price if gain of 20% is made on a good sold at Rs. 300
275
250
300
360

ANS.250

Q4: Find cost price if loss of 20% is made on a good sold at Rs. 300
360
250
375
320

ANS.3

Q5: When a item is sold for 10% gain and other for 10% loss, the seller incurs
loss of 1%
profit of 1%
loss of 2%
profit of 2%

ANS.LOSS of 1%