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)
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
.
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
Find the profit percent or loss percent in the given case:
CP=Rs 400, Profit=Rs 80
Find the profit percent or loss percent in the given case:
CP=Rs 275, loss=Rs 25
Find the profit percent or loss percent in the given case:
SP=Rs 320, Gain=Rs 70
Find the profit percent or loss percent in the given case:
SP=Rs 250, Loss =Rs 50
Find the profit percent or loss percent in the given case:
CP = Rs 400, SP = Rs 475
A man purchased a bicycle for Rs 2000 and sold it for Rs 2400.Find his gain percent.
Sabina bought refrigerator for Rs 9900 and sold it for Rs 9000. Find her loss percent.
The cost price of 11 pens is equal to the selling price of 10 pens. find the gain or loss percent.
Renu bought a bicycle for Rs 5000 and sold it at a profit of 8%.Find her selling price.
Tripti bought a television for Rs 20000 and sold it at a loss of 12% find the selling price of the television.
Tripti bought a television for Rs 20000 and sold it at a loss of 12% find the selling price of the television.
By selling an article for Rs 864, a shopkeeper earns a profit of 8%, Find the cost price.
A man sold the radio at the loss of 12 %. If the selling price was Rs 7040, what was its cost price?
Riya sold a bicycle at a loss of 20 %. If she sold it for Rs 800 more, she would have received a profit of 5%. Find the cost price.
Ujila sold her gold necklace at a profit of 7%. If she had sold it for Rs 294 more she would have got 10% profit. Find the cost price of the necklace.
A wholesaler marks the price of his goods 40% above the cost price and allows 20% discount. If his purchase price of an item is Rs, 1000, how much should a customer pay for it with 15% tax?
ASK ANY QUESTION ON Profit and Loss
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Mar 21, 2018
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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.
Mar 26, 2017
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pratham
formula of C.P
Mar 18, 2017
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what is formulae of discount
Feb 07, 2017
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