Here are some solved examples on Profit and Loss :
Example. 1 : A man buys an article for Rs. 75 and sells it for Rs. 90. Find his gain percent ?
Solution :
C.P = Rs. 75 and S.P = Rs. 90
So, gain = Rs. (90 - 75) = Rs. 15
Gain % = (15/75 × 100) % = 20%
Example. 2 : A person incurs 10% loss by selling a bat for Rs. 900. At what price should the bat be sold to earn 10% profit ?
Solution :
The C.P of the bat = 100/90 × 900 = Rs. 1000
To earn 10% profit the bat must be sold at = 1000 × 110/100 = Rs. 1100
Example. 3 : A Man sold an article at a profit of 10%. If he had sold it Rs. 4.80 more, he would have gain 18%. What is the cost price ?
Solution :
Let the C.P of the article be Rs. X. Then,
110% of X + 4.80 = 118% of X
or, 118% of X - 110% of X = 4.80
or, 8% of X = 4.80
or, X = (4.80 ×  ) = Rs. 60
Example. 4 : If the C.P of 15 books is equal to the S.P of 10 books. Find the gain% or Loss% ?
Solution :
Let the C.P of each book be Rs. 1. Then,
C.P of 10 books = Rs. 10
and C.P of 15 books = Rs. 15 = S.P of 10 books (according to the question)
Now, We have C.P of 10 books = Rs. 10
and S.P of 10 books = Rs. 15
Then, gain = Rs. (15 - 10) = Rs. 5
.'. Gain % = [(gain/C.P) x 100]% = (5/10) x 100 = 50%
Example. 5 : A person bought 6 pens for Rs. 10 and sold 4 pens for Rs. 6. Find his gain% or loss% ?
Solution :
Let, number of pens bought = L.C.M of 6 and 4 = 12
.'. C.P = Rs. (10/6)x12 = Rs. 20; S.P = Rs. (6/4) x 12 = Rs 18
Here we can see C.P > S.P
So the person incured a loss
.'. Loss% = (2/20) x 100 = 10%
Example. 6 : A dishonest shopkeeper sells his goods at cost price but uses a weight of 900 gms for a Kg. Find his Gain% ?
Solution :
1 Kg = 1000 gms
By the formula Gain% = [(Error)/(True Value) - (Error)] x 100 %
.'. [(100/900)x 100]% = 100/9 % =  %
Example. 7 : If the marked price of an article is 20 % more than its C.P and a shopkeeper allows a discount of 10%. Then find his profit percent ?
Solution :
Let the C.P be Rs. 100. Then,
M.P = Rs. 120
After 10% discount S.P = 120 × 90% = 120 × 9/10 = Rs. 108
.'. Profit % = [(108 - 100)/100] × 100 % = 8%
Example. 8 : Amit sold two flats for Rs. 12,50,000 each. On one he gains 15% while on the other he loses 15%. How much does he gain or lose in the whole transaction ?
Solution :
We know that in such a case , there is always a loss.
.'. Loss% = [(Common Loss% or Gain%)/10]2 = [15/10]2 % = 2.25%
Example. 9 : At what percentage above the C.P must an article be marked so as to gain 35% after allowing a customer a discount of 10% ?
Solution :
Let the C.P be Rs. 100. Then S.P = Rs. 135
Also let M.P be Rs. X.
Then, 90% of X = 135
or, X = 135 x 100/90 = 150
.'. Marked Price = 50% above C.P.
Example. 10 : A Shopkeeper marks all his goods at 50% above the C.P and thinking that he will still make 25% porfit, offers a discount of 25% on the marked price. What is his actual profit in the sale ?
Solution :
Let the C.P be Rs. 100. Then, M.P = Rs. 150
S.P = 75% of Rs. 150 = Rs. 112.50
.'. Gain % = 12.50%
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