# Arithmetic

#### Simple Interest & Compound Interest - 1

Profit And Loss : 1

Profit And Loss

This chapter forms the bedrock of every economic transaction taking place between two entities or multiple parties. The concepts of this chapter form the foundation of every dealing taking place through-out the world. But, as per our scope we will deal with only the basics of it stick to what is usually asked in the CAT or other B-school exams. Before we go into problem solving, there are a few terms whose understanding is crucial.

Cost Price:

The cost price or C.P.is defined as the cost at which a buyer buys a product or the cost involved in the manufacturing of a product.

Selling Price:

The selling price or S.P. is defined as the price at which a seller sells his goods or a manufacturer sells his goods.

Profit: The difference between the S.P. and C.P. is known as profit.

Loss: The difference between the C.P. and S.P. is known as loss.

If the cost price is more than the selling price, then loss is said to have been incurred where as if the selling price is more than the cost price, then profit or gain is incurred in the transaction.

So, one can say that the value of profit percentage depends on the ratio of S.P. and C.P. and not just on their absolute values.

Example 1: Ravi bought a watch and paid 20% less than its original price. He sold it at 30% profit on the price he had paid. Then, what is the profit percentage earned by Ravi on the original price of the watch?

Solution: Let the original price of the watch be Rs 100

His C.P. = 0.8 * 100 = Rs 80

He makes a profit percentage of 30%, so his S.P. = 1.3*80 = Rs 104

Profit percentage on original price = {(104-100)/100}*100 = 4%

Example 2: If the profit percentage is 20% calculated on the C.P., then what is the profit percentage calculated on the S.P.?

Solution: Let the C.P = Rs 100

S.P. = 1.2* 100 = Rs 120

Profit = 120-100 = Rs 20

Profit % on S.P. = (20/120)*100 = 16.66%

Example 3:  Akash wants to sell a camera at a profit of 20%. He bought it at 10% less and sold it Rs 30 less but still he gained 20%. Then, what is the C.P. of the camera?

Solution: Let the C.P. of the camera = Rs x

S.P. of the camera = 1.2x

New C.P. = 0.9*x = 0.9x

New S.P. = 1.2*(0.9x) = 1.08x { As profit % is still 20}

According to the given condition, 1.08x = 1.2x – 30

Or x = Rs 250

Thus, the C.P. of the camera was Rs 250.

Example 4:  A fruit vendor makes a profit of 25% by selling oranges at a certain price. If he charges Re1 more on each orange, he would have gained 50%. What was the initial S.P. of each orange?

Solution: Let the C.P. of each orange = Rs x

Initial S.P. = 1.25x

Now he increases the S.P. by Re1

New S.P. = 1.25x + 1

Profit % = 50%

1.5x = 1.25x + 1   or o.25x = 1 or x = 4

New S.P. = 1.25*4 = Rs 5

Example 5: If the cost price of 10 articles is equal to the S.P. of 9 articles. Then what is the profit or loss percentage?

Solution: Let the C.P. of 1 article is Re 1

C.P. of 10 articles = Rs 10 = S.P of 9 articles

S.P. of 1 article = 10/9

Profit % = {(10/9) – 1}*100 = 11.11%

Example 6: By selling 144 chairs, Arvind suffered a loss equal to the selling price of 6 chairs. What is his loss percentage?

Solution:  Let the S.P. of 1 chair = 1 Re

Total loss = S.P. of 6 chairs = Rs 6

Total C.P. = Total S.P + Total loss

= 144 + 6 = Rs 150

Loss % = (6/150)*100 = 4%

Example 7:  A man sells a shirt for Rs 144 where by his profit percentage was numerically equal to its cost price. Then, what was the cost price of the shirt?

Solution:  Let the C.P. of the shirt = Rs x

S.P. = Rs 144 and profit % = x%

144 = x( 1+ x/100)

14400 = x(100+x)

Or   x2 + 100x – 14400

x2 + 180x – 80x – 14400

Thus, x = 80

Example 8: A dealer sold a printer at a profit of 10%. If he had bought the bicycle at 10% lesser price and sold it at a price which is 60 more than the original selling price thereby gaining 25% on the transaction, what was the original price of the printer?

Solution:

Let the original price of the printer = Rs x

S.P. = 1.1x

New C.P. = 0.9x

New S.P = 1.1x + 60

But now the profit percentage = 25%

0.9x * 1.25 = (1.1x + 60)

1.125x = 1.1x + 60

0.025x = 60

Or x = Rs 2400

Example 9: The ratio in which sugar A at Rs 32 per kg must be mixed with sugar B at Rs 25 per kg so as to gain 20% by selling the mixture at Rs 32.40 per kg is-

Solution: Selling price = 32.40/kg, gain % = 20

C.P. of the mixture = 32.40/1.2 = Rs 27/kg

Let V1 is the quantity of sugar A and V2 is the quantity of sugar B to be mixed

32V1 + 25V2 = 27V1 + 27V2

5V1 = 2V2

Or V1:V2 = 2:5

Thus sugar A and sugar B must be mixed in the ratio of 2:5.

(This problem can also be solved using the concepts studied in Mixtures and Alligations)

Example 10: Sunny buys some bananas and by selling 40% of them he realizes the cost price of all the bananas. The next day he found that the bananas begin to rot and so he sells 80% of the remaining bananas at half the previous rate of profit and the rest he throws away. What was the overall profit percentage of Sunny?

Solution:  Let’s assume that Sunny buys 100 bananas at 1 Re each.

So, CP of 100 bananas = Rs 100 = S.P. of 40 bananas

S.P. of 1 banana = 100/40 = Rs 2.5

Profit% = (2.5/1 – 1)*100 = 150%

Remaining bananas = 60

Out of these he sold 80%, i.e. 0.8 *60 = 48 bananas at half the rate of earlier profit i.e. at 75%

S.P. = 1.75 * 48 = 84

Total S.P. = 100 + 84 = 184, Total C.P. = 100

So, overall profit % = 84%