## Note on Profit and Loss

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• Exercise
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The producerproduces a goods at some certain cost. When those goods are sold at a higher price than the production price, then there is profit. And, if the goods are sold at lower price than production cost, then he suffers a loss.

Thus, profit = Selling price - Cost price

or,Profit = S.P - C.P

Loss = Cost Price - Selling Price

or, Loss= C.P - S.P

For example:

If Renu bought a book for Rs 500 and sold it for Rs 600, then she made a profit of Rs 100 i.e profit = Rs 100

Similarly, if Ritesh bought a machine for Rs 200 and sold it for Rs 100, then he suffered a loss of Rs 100. i.e loss = Rs 200 - Rs 100 = Rs 100 (loss)

### Profit Percentage and Loss Percentage

For the purpose of comparison, we usually express the actual profit or loss as a percentage of a cost price.

For example; Samikshya sold a bag for Rs 60 which costs Rs 50 and shoes sold for Rs 110 which costs Rs 100. In each case, the shopkeeper makes a profit of Rs 10. It seems that in both cases profit is equally gained.

But in percentage we have:

In the first case, profit percentage = $$\frac{10}{ 50}$$ x 100 = 20 %

In the second case, profit percent = $$\frac{10}{100}$$ x 100 = 10 %

Hence, in the first case, she made more profit than in the second case, it is better and accurate method of comparison.

Have a look at these formulas:

Percentage profit = $$\frac{actual\;profit}{C.P}$$ x 100

Percentage loss = $$\frac{actual\;loss}{C.P}$$ x 100

Examples

1. A pen costing Rs 28 sold for RS 36. Find the percentage profit.
Solution:
Cost price (CP) = RS 28
Selling price(SP) = Rs 35
Actual profit = SP - CP = Rs 35 - Rs 28 = Rs 7
Percentage profit= $$\frac{actual \;profit}{CP}$$×100 =$$\frac{7}{28}$$×100 =25%

2. A book costing Rs 60 sold for Rs 50. Find the percentage loss.
Solution:
Cost price (CP) = Rs 60
Selling price (SP) = Rs 50
Actual loss = CP - SP = Rs 60 - Rs 50 = Rs 10
Percentage loss = $$\frac{actual \;loss}{CP}$$×100 =$$\frac{10}{60}$$×100 =16$$\frac{2}{3}$$%

• The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
• The price, at which an article is sold, is called its selling prices, abbreviated as S.P.
• If S.P. is greater than C.P., the seller is said to have a profit or gain.
• If S.P. is less than C.P., the seller is said to have incurred a loss.
• Loss or gain is always reckoned on C.P.

.

### Very Short Questions

Solution:

Given information,

Cost Price (CP) = Rs 28

Selling Price (SP) = Rs 35

Here,

Actual Profit = SP - CP = Rs 35 - Rs28 = Rs 7

Now,

Percentage Change = $$\frac{actual profit}{CP}$$ × 100

= $$\frac{7}{28}$$× 100

= 25%

Solution;

Given information,

Cost Price (CP) = Rs 60

Selling Price (SP) = Rs 50

Here,

Actual Loss = CP - SP

= Rs 60 -Rs 50

= Rs 10

Now,

Percentage Loss = $$\frac{actual loss}{CP}$$× 100

= $$\frac{10}{60}$$×100

= 16 $$\frac{2}{3}$$ %

Solution:

Let the cost price be Rs x.

Then, profit = 30% of x

= $$\frac{30}{100}$$× x

= $$\frac{3x}{10}$$

Now,

CP = SP - Profit

or, x = 65 - $$\frac{3x}{10}$$

or, x + $$\frac{3x}{10}$$ = 65

or, $$\frac{10x+3x}{10}$$ = 65

or, 13x = 650

or, x = $$\frac{650}{13}$$

$$\therefore$$ x = 50

Hence, cost of the book = Rs 50

Solution:

Selling price of sari = Rs 1350

Profit (P) = Rs 150

Cost price of sari (CP) =?

We know that,

Profit = SP - CP

or, 150 = 1350 - CP

or, CP = 1350 -150

or, CP = 1200

∴ Cost Price (CP) of sari = Rs 1200

Solution:

Given,

Cost Price of the Calculator (CP) = Rs 760

Loss = Rs 50

Selling Price (SP) = ?

We know that,

Loss = CP - SP

or, 50 =Rs 760 - SP

or, SP = Rs 760 - Rs 50

or, SP = Rs 710

∴ Selling Price of the Calculator (SP) = Rs 710

Solution:

Given information,

Marked Price = Rs 450

Discount amount = 20% of RS 450

= $$\frac{20}{100}$$× 450

= Rs 90

Here

Selling Price = Marked price - Discount amount

= Rs 450 - Rs 90

= Rs 360

Solution:
Given information,

Marked Price = Rs 250

Selling Price (SP) = Rs 200

Discount = MP - SP

= Rs 250 - Rs 200

= RS 50

Here,

Discount Percentage = $$\frac{discount}{MP}$$× 100

= $$\frac{50}{250}$$× 100

= 20%

Solution:

Given information,

Selling Price = Rs 342

Let the marked price be x.

Then,

Discount amount = 10% of x

= $$\frac{10x}{100}$$

= $$\frac{x}{10}$$

Marked Price = SP + Discount amount

or, x = 342 + $$\frac{x}{10}$$

or, x - $$\frac{x}{10}$$ = 342

or, $$\frac{10x -x}{10}$$ = 342

or, 9x = 3420

$$\therefore$$ x = $$\frac{3420}{9}$$ 380

Hence, the marked price of the Article = Rs 380

Solution:

Given information,

Selling Price (SP) before VAT = Rs 4500

Selling Price (SP) after VAT = Rs 5000

VAT amount = SP with VAT - SP before VAT

= Rs 5400 - Rs 5000

= Rs 400

$$\therefore$$ VAT rate = $$\frac{VAT amount }{SP before VAT}$$× 100

= $$\frac{400}{5000}$$× 100

= 8%

Solution:

Given information,

Marked Price = Rs 1,250

Discount Percent = 5%

Actual Price of watch = MP - Discount Percentage

= Rs 1,250 - Rs 1,250 × $$\frac{5}{100}$$

= Rs 1,250 - Rs 62.50

= Rs 1,187.50

∴ Actual Price of watch = Rs 1,187.50

Solution:

Given information,

Marked Price of Radio(MP) = Rs 1160

Selling Price after discount (SP) = Rs 1044

Now,

Discount = MP - SP

= Rs 1160 - Rs 1044

= Rs 116

∴ Discount Percentage = $$\frac{Discount Amount}{MP}$$× 100

= $$\frac{116}{1160}$$ × 100

= 10%

Solution:

Given information,

Marked Price (MP) = Rs 210

Discount Percent = 12%

Discount amount = 12% of MP

= 210× $$\frac{12}{100}$$

= Rs 25.20

∴ Actual Price of the Book = Marked Price - Discount

= Rs 210 - Rs 25.20

= Rs 184.80

0%

30%
25%
20%
15%

9.09%
12%
15%
10%

25%
20%
28%
15%

16.25%
16.67%
15.67%
14%

18.75%
15.35%
19.70%
28.25%

20%
10%
30%
25%

5.25%
9.095%
8%
8.85%

12.25%
10%
8%
5%

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Rs 17600
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Rs 500
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Rs 8500
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Rs 3200
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Rs 3300

Rs 9800
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Rs 2300
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Rs 1610
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##### Anoj

1. a man sells a tv for rupees 3450and makes a profit of 15% . he sells a second tv set at a loss of 10%.if on the whole he neither gains nor loses , find the cost price of the second tv.