Shortcut – Profit, Loss and Discount
Profit or Loss Percentage:
Profit or Loss Percentage=$\dfrac{S.P-C.P}{C.P} \times 100$
S.P – Selling Price.
C.P – Cost Price.
Question:
A bike worth Rs. 40000 is sold for Rs. 46000. What is the profit percentage?
Answer:
S.P = 46000;
C.P = 40000
Substitute the values in the above equation, we get
P% = [(46000-40000)/40000]x100
= 15% profit
Question:
A mobile phone worth Rs. 9900 is sold for Rs. 9000. What is the percentage loss?
Answer:S.P = 9000;
C.P = 9900
Substitute the values in the above equation, we get
L% = [(9900-9000)/9900] x 100;
L% = 9.09% loss
Shortcut – Profit, Loss and Discount
Net Profit or Loss Percentage when two changes are made.
a = percentage profit or loss in the first case.
b = percentage profit or loss in the second case.
Substitute ‘+’ for profit percentage.
Substitute ‘-‘ for loss percentage.
Question:
A product worth $ 3000 is sold for 10% profit and then for 20% loss. What is the overall profit or loss percentage in the sale?
Answer:Net change = 10 – 20 + [(10)(-20)/100]
= -12
The value obtained is negative.
This indicates that a loss is incurred in the sale.
12% loss.
Shortcut – Profit, Loss and Discount
Finding selling price after multiple changes.
(a, b and c) are the profit or loss percentages.
The formula can be expanded or reduce according to the number of changes given in the question.
Substitute ‘+’ for profit percentage.
Substitute ‘-‘ for loss percentage.
Question:
A watch worth Rs. 5000 is sold by A to B at 10% loss. B sold it to C at 30% loss. C sold it to D at 40% profit. What is the price at which D bought the watch?
Answer:a = -10; b = -30; c = 40
C.P = 5000
Substitute the values in the above equation, we get
S.P = (9/10)(7/10)(14/10) x 5000
S.P = 4410
Shortcut– Profit, Loss and Discount
Steady Profit or Loss.
a – steady rate of profit or loss percentage.
Substitute ‘+’ for profit percentage.
Substitute ‘-‘ for loss percentage.
n – Number of times the percentage change occurs.
Question:
The price of a laptop decreases by 20% every year. It the laptop was bought for Rs. 45000, at what price will it be sold after 2 years?
Answer:a = -20
C.P = 45000
Substitute the values in the above equation, we get
S.P = 45000[0.8]2
S.P = 28800
Selling price after two years
= Rs. 28800
Shortcut– Profit, Loss and Discount
Net gain or loss percentage when (a %) profit and (a %) loss occurs.
a – percent loss and percentage gain.
Question:
Two laptops were sold for the same selling price. The first one is sold at 50% profit and the second one is sold at 50% loss. Due to this sale what is the profit or loss percentage incurred by the seller?
Answer:Assume that the selling price of each laptop = Rs. 150
Cost price of first laptop:
150 = (150/100)CP
C.P1 = 100
Cost price of second laptop:
150 = (50/100)CP
C.P2 = 300
Total cost price = 100 + 300 = 400
Total selling price = 150 + 150 = 300
Loss % = (100/400)100 = 25%
(Or)
$(a^{2}/100)% loss = (50^{2}/100)%loss = 25% loss.$
Note:
Shortcut applicable only when selling price of both products are equal.
Shortcut– Profit, Loss and Discount
Discount, Marked Price and Selling Price.
d – Discount percentage M.P = Marked price or Market price of the product
Question:
A product is marked Rs. 450 by the seller. If he sells at a price of Rs. 330, what is the discount provided in percentage?
Answer:M.P = 450
S.P = 330
Substitute the values in the above equation, we get
D% = [(450-330)/450]x100
D% = 26.67%
Discount provided in percentage = 26.67%
Profit and loss concepts:
1. One can generate a profit only if Selling Price> Cost Price
2. One generates a loss when Selling Price < Cost Price.
3. Profit = Selling Price – Cost Price
%profit = {(Selling Price – Cost Price)/Cost Price} x 100
4. Loss = Cost Price – Selling Price
%Loss = {(Cost Price – Selling Price)/Cost Price} x 100
5. Sale price :- If there is a profit of P %,
Cost Price = C Then SP = {(100+P)/100}xC
6. If there is a loss of L %,
Cost Price = C
Then
SP = {(100-L)/100}xC
7. Cost price :-
If there is a profit of P %,
Cost Price = C
Sale price= SP
Then C = {100/(100+p)} x SP
If there is a loss of L %,
Then
C = {100/(100-L)}xSP
8. A dishonest dealer claims to sell his goods at cost price ,but he uses a weight of lesser weight .Find his gain%.
Formula:$Gain % =\dfrac{true weight -false weight}{false weight}\times 100$
9. A shopkeeper sells an item at a profit of x % and uses a weight which is y % less .find his total profit
Formula:$Gain % =\dfrac{%profit+%less in weight}{100-%less in weight}\times 100$
10. When dealer sells goods at loss on cost price but uses less weight .
Formula: $Profit % or Loss % =\dfrac{%less weight -%loss}{100 -%less weight}\times 100$
11. A dishonest dealer sells goods at x % loss on cost price but uses a gm instead of b gm . his profit or loss percent :-
Formula: $Profit % or Loss%=[100-loss%]\dfrac{original weight }{altered weight}- 100$
Note :- profit or loss will be decided according to sign .if +ive it is profit ,if –ve it is loss .
12. If the price of an item increases by r% , then the reduction in consumption so that expenditure remains the same ,is
Formula: $\dfrac{r}{100+r}\times 100%$
13. If the price of a commodity decreases by r% then increase in consumption , so as not to decrease expenditure on this item is
Formula:$\dfrac{r}{100-r}\times 100%$
14. A reduction of x% in price enables a person to buy y kg more for Rs. A. Then the
Formulas:(1)Reduced Price=$\dfrac{x}{100y}\times A$
(2)Original Price=$\dfrac{x}{(100-x)y}\times A$
15. When there are two successive profits of x% and y% then the net percentage profit =[x+y +xy/100]
When there is a profit of x% and loss of y% then net percentage profit or loss = [x – y – xy/100]
Note: If the final sign in the above expression is positive then there is net profit but if it is negative then there is net loss.
16. A sells goods to B at a profit of x% andB sells it to C at a profit of y%. If C pays RsP for it,then the cost price for A is
$Rs.[\dfrac{100\times 100\times P}{(100+x)(100+y)}]$
Note:- for loss replace plus sign with minus .
17. When each of the two things is sold at the same price,and a profit of p% is made on the first and a loss of L% is made on the second,then the percentage gain or loss is .
Formula:$\dfrac{100(P-L)-2PL}{(100+P)+(100-L)}$
18. If profit percentage and loss percentage are equal, put P=L
=> $%loss = p^{2} /100$
19.Selling Price=Marked Price-Discount
20.$Selling Price=Market Price (\dfrac{100-Discount }{100})$
(OR)$Selling Price=Cost Price(\dfrac{100+Profit}{100})$
Question:
A person purchased an article for ₹ 150. If he sells it at a 20% profit then find his selling price.
Solution : Formula :
SP = CP [ 1 + ( Gain % x 100) ]
SP = 150 [ 1 + (20/100) ]
= 150 x 1.2 = 180.
The article selling price is ₹ 180.
Question:
By selling a watch for ₹ 990, a shopkeeper incurs a loss of 10%. Find the cost of the watch for shopkeeper.
Solution : Formula :
SP = CP x [ 1 – ( Loss % x 100) ]
990 = CP x [ 1 – (10/100) ]
CP = 990 / 0.9 = 9900 / 9 = ₹ 1100.
Question:
By selling a product for ₹ 720, a loss of 10% is obtained. At what price the product must be sold to get 20% gain?
Solution :Formula for first case SP = CP + [ 1 – ( %Loss x 100) ]
720 = CP + ( 1 – 0.1 )
CP = 720 / 0.9 = ₹800.
Formula for second case SP = CP [ 1 + ( Gain % x 100) ]
SP = 800 [ 1 + (20/100) ]
= 800 x 1.2 = ₹ 960.
I.e The seller sold the product at ₹ 960 then he will gain 20%.
Question:
A person sold an article at 12% profit. Had he sold it for ₹ 18. more he would have gained 18%. What is the cost price of the article?
Answer:Formula :- SP = CP [ 1 + ( Gain % x 100) ]
In first case
SP = CP ( 1 + 0.12) = 1.12 CP
In second case
SP = CP ( 1 + 0.18) = 1.18 CP
So the difference between first and second case is ₹ 18.
i.e 1.18CP – 1.12CP = 18.
CP = 18 / 0.06 = 1800 / 6 = 300.
The article cost price is ₹ 300.
Question:
A manufacturer sold a product for ₹ 2400 and made a profit of 25% in the process. Find his profit percent if he had sold his goods for ₹2040.
Answer :Formula – SP = CP [ 1 + ( Gain % x 100) ]
In first case SP = 2400
2400 = CP [1 + (25/100) ]
CP = 2400 / 1.25 = 240000 / 125 = 1920.
In second case SP = 2040.
Then Profit = 2040 – 1920 = 120.
Profit % = [ Profit x 100] / CP
= 120 x 100 / 1920 = 6.25 %.
Question:
Tom sells a bicycle to Ram at 25% profit, Ram sells it to Hari at 20% loss. If Hari pays ₹1500 for it, at what price Tom purchase it?
Answer :First find the Ram cost price and Ram sold price ₹ 1500
Formula : SP = CP [ 1 – ( %Loss x 100) ]
1500 = CP [ 1 – (20 / 100) ]
CP = 1500 / 0.8 = 15000/ 8 = 1875.
Here Ram cost price equal to Tom sell price.
In second case Tom got 20% profit and his sell price ₹ 1875.
SP = CP [ 1 + ( Gain % x 100) ]
1875 = CP [ 1 + (25/100) ]
CP = 1875 / 1.20 = 187500 / 125 = 1500.
Question:
A fruit vendor recovers the cost of 25 mangoes by selling 20 mangoes. Find his profit percent.
Answer:Formula – The Profit percent = [ mangoes left / mangoes Sold ] x 100.
Profit % = [ ( 25 -20) / 20 ] x 100 = 25%
The fruit vendor profit is 25%.
Question:
If the cost of 20 pens is equal to the selling price of 16 pens. what is the gain or loss%
Answer:Here The cost pens less than the selling pens, so in this process get profit
Formula :- The Profit percent = [ pens left / pens Sold ] x 100.
Profit % = [ ( 20 -16) / 16 ] x 100 = 400 / 16 = 25%
The profit is 25%.
Question:
While selling of 5 pens, A person get profit equal to selling of 2 pens. Find the profit percent.
Answer : Write the profit equation.
Selling Price = Profit + Cost Price
5 SP = 2SP + 5CP
3 SP = 5CP
SP / CP = 5 / 3
The Profit percent = [ pens left / pens Sold ] x 100.
Profit % = ( 2 / 3 ) x 100 = 200 / 3 = 66.66%.
Question:
While selling of 5 pens, A person incurred loss equal to sold of 3 pens. Find the loss percent.
Answer : Write the loss equation. Selling Price = Cost Price – Loss
5 SP = 5CP – 3SP
8 SP = 5CP
SP / CP = 5 / 8
Loss % = ( 3/ 8 ) x 100 = 300 / 8 = 37.5%.
Question:
While selling of 6 pens, A person get profit equal to cost of 2 pens. Find the profit percent.
Answer : Write the profit equation.
Selling Price = Profit + Cost Price
6 SP = 2CP + 6CP
6 SP = 8 CP
The Profit percent = [ pens left / pens Sold ] x 100.
Profit % = ( 2 / 6 ) x 100 = 200 / 6 = 33.33%
Question:
While selling of 10 pens, A person incurred loss equal to cost price of 3 pens. Find the loss percent.
Answer : Write the loss equation.
Selling Price = Cost Price – Loss
10 SP = 10CP – 3CP
10 SP = 7 CP
SP / CP = 7 / 10
Loss % = ( 3/ 10 ) x 100 = 300 / 10 = 30%.