# Profit and Loss The terms Profit and Loss are used in businesses. In business transactions, goods are purchased and sold. The price used to purchase is called “Cost Price” and written as CP. The price obtained by selling goods is called “Selling Price” and it is written as SP.

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If the selling price of certain item is more than the cost price, then there is a profit. If the cost price of certain item is more than its selling price, then there is a loss. For example:

-    An article is bought for Rs. 500 and sold it for Rs. 600. Here, SP is more than CP, so there is a profit of Rs. 600 – 500 = Rs. 100

-    An article is bought for Rs. 1000 and sold for Rs. 800. Here, CP is more than SP, so there is a loss of Rs. 1000 – 800 = Rs. 200 As stated in the examples above,

If SP>CP, there is a profit and it is obtained as

Profit (P) = SP – CP

If CP>SP, there is loss and it is obtained as

Loss (L) = CP – SP

Profit and loss percent is calculated on the basis of cost price (CP). So, ## The formula of CP, SP, Profit, and Loss: ## How to solve the problems related to Profit and Loss?

While solving the problems related to profit and loss we must use the following steps:

i.     Understand the problem and make planing.

ii.    Solve problem according to the planing.

iii.  Review solved problem and recheck  it.

iv.  At last, write the conclusion according to the question.

### Worked Out Examples

Example 1: Mrs. Sarala bought a Banarasi Sari at Rs 3500. After one month, she was interested to have a new one and hence she sold it for Rs. 3200. Find her loss percent.

Solution: Here, Her loss percent is 8.57%.

Example 2: Sabin bought 14 copies for Rs. 140 and sold 8 copies for Rs. 96. Find his profit or loss percent.

Solution: Here, He has got a profit of 20%.

Example 3: An exercise book cost Rs. 20. If it is sold at a profit of 10%, find its selling price.

Solution: Here, The selling price of that exercise book is Rs. 22.

Example 4: If a shopkeeper sells a shirt for Rs. 270 at a loss of 10%, for what price should it be sold, so as to get a gain of 30%?

Solution: Here, The shirt should be sold at Rs 390 to get a profit of 30%.

Example 5: Salman sold a DVD at a gain of 8%. Had it been sold for Rs. 75 more, the gain would have been 14%. Find the cost price of the DVD.

Solution: Here, Hence, the CP of the DVD is Rs. 1250.

Do you have any questions regarding the Profit and Loss?

You can ask your questions or problems in the comment section below.

1. A man allows a discount of 10% on a book whose marked price is ₹40. What is the cost price so that the profit is 20% ?

1. Solution: Here,
MP = ₹40
Discount = 10%

SP = (100 – d%)MP/100 = (100 – 10)40/100 = 90×40/100 = ₹36
Profit = 20%

CP = 100SP/(100+P%) = 100×36/(100+20) = 3600/120 = ₹30

∴ The cost price is ₹30. Ans.

2. price of a pen is 240 with discount perfect of 5%. What amount shoult be paid when discount would be 10%?

1. Solution: Here,
1st Case,
SP = 240
Discount = 5%
MP = [100/(100-d%)] × SP = [100/95] × 240 = 252.63
2nd Case,
MP = 252.63
Discount = 10%
SP = [(100-d%)/100] × MP = [90/100] × 252.63 = 227.36

∴ 227.36 should be paid.

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4. An article was sold for 10% discount there is a profit of 5%.if the same article is sold at 5% discount there will be Rs 251 profit.find the marked price and cost price

1. Solution:
Here,
MP = Rs. x (let)

1st Case,
Discount = 10%
∴ SP = (100-d%)/100 × MP = 90x/100
Profit = 5%
∴ CP1 = 100/(100+P%) × SP = 6x/7

2nd Case,
Discount = 5%
∴ SP = (100-d%)/100 × MP = 19x/20
Profit = Rs. 251
∴ CP2 = SP – Profit = 19x/20 – 251

But, CP is the same,
∴ CP1 = CP2
i.e. 6x/7 = 19x/20 – 251
or, 6x/7 = (19x – 5020)/20
or, 120x = 133x - 35140
or, 120x – 133x = – 35140
or, -13x = -35140
or, x = -35140/-13
or, x = 2703.07

∴ MP = x = Rs. 2703.07
∴ CP = 6x/7 = Rs. 2316.90

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6. A man bought two school bags for RS.2020.He sold one of them at 20% profit and the other at 20% loss.Find his gain or loss percent in this transaction if the selling prices of both bags are same.

1. Solution: Here,
Total CP = Rs. 2020

For 1st bag,
CP = Rs. x (let)
Profit = 20%
∴ SP = (100+P%)CP/100 = (100+20)x/100 = 120x/100 = 6x/5

For 2nd bag,
CP = Rs. 2020 – x
Loss = 20%
∴ SP = (100 – L%)CP/100 = (100 – 20)(2020 – x)/100 = (8080 – 4x)/5

Both the SP are same,
∴ 6x/5 = (8080 – 4x)/5
Or, 6x = 8080 – 4x
Or, 6x + 4x = 8080
Or, 10x = 8080
Or, x = 8080/10
Or, x = 808

∴ Total SP = 2×6x/5 = 2×6×808/5 = Rs. 1939.2

CP > SP, so there is loss.
∴ Loss = SP – CP = Rs. 1939.2 – 2020 = Rs. 80.8

∴ Loss % = Loss × 100/CP = 80.8×100/2020 = 4%

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9. A shopkeeper adds 30% on the cost price of any article for m.p and sells allowing 10% discount . If his cost price for an article is Rs 24000 then find its actual selling price.

1. Solution:
Here,
CP = Rs. 24000
MP = CP + 30% of CP = Rs. 24000 + (30/100) × 24000 = Rs. 31200
Discount = 10%

Actual SP = MP – Discount
= Rs. 31200 – 10% of 31200
= Rs. 31200 – (10/100) × 31200
= Rs. 28080 Ans.

10. Ananta purchased one scocetage peroter at Rs 65000 and other at Rs.75000. Find his profit and loss percentage if he sold both at the rate of Rs. 72000 each.

1. Solution:
Here,
Total CP = Rs. 65000 + 75000 = Rs. 140000
Total SP = Rs. 72000 × 2 = Rs. 144000

SP > CP, so there is profit,

Profit = SP – CP = Rs. 144000 – 140000 = Rs. 4000

Profit % = (Profit/ CP) × 100%
= (4000/140000) × 100%
= 2.85% Ans.

11. A shopkeeper allows a discount of 10% on the marked price , he still makes a gain of 12.5%. By what percent the marked price above the cost price.

1. Solution:
Here,
MP = x (let)
Discount = 10%
SP = MP – Discount = x – 10% of x = x – 10x/100 = 90x/100
Profit = 12.5%

CP = (100/100 + P%) × SP = (100/100+12.5) × 90x/100 = 90x/112.5

Percent above = (MP – CP)×100%/CP
= (x – 90x/112.5)×100%/(90x/112.5)
= 2250x/90x
= 25% Ans.

12. A TV was sold at Rs. 43200 by adding 20% VAT after 10% discount. What is the
discount allowed on the TV ?

1. Solution:
Here,
SP with VAT = Rs. 43200
Discount = 10%
VAT = 20%

By formula,
MP = 100×100×SP with VAT /(100-d%)(100+v%)
= 100×100×43200/(100-10)(100+20)
= 432000000/90×120
= Rs. 40000

Now,
Discount = 10% of MP
= 10×40000/100
= Rs. 4000

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