Cost Price = C.P.
Selling Price = 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.
If an article is sold at a gain of say 25%, then S.P. = 125% of C.P.
If an article is sold at a loss of say, 25% then S.P. = 75% of C.P.
Loss or gain is always reckoned on C.P.
1. Gain = S.P.  C.P.
2. Loss = C.P.  S.P.
3. Gain Percentage:
Gain % =Gain x 100/C.P.
4. Loss Percentage:
Loss % = Loss x 100/C.P.
5. Selling Price: (S.P.)
S.P. = (100 + Gain %)/100 X C.P
6. Selling Price: (S.P.)
S.P. = (100  Loss %)/100 X C.P.
7. Cost Price: (C.P.)
C.P. = 100/(100 + Gain %) X S.P.
8. Cost Price: (C.P.)
C.P. = 100/(100  Loss %) X S.P.
9. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by:
Loss % = (Common Loss and Gain %/10)^{2} = (x/10)^{2}
10. If a trader professes to sell his goods at cost price, but uses false weights, then
Gain % = [Error/(True Value)  (Error) X 100]%
1. 

CP = Rs 27.50,
SP = Rs 28.60
So, Gain = Rs (28.60  27.50) = Rs 1.10
∴ Gain% = (1.1027.50 x100)% = 4%
2. 

Let the new SP be Rs x Then,
(100  loss%) : (1st SP) = (100 + gain%) : (2nd SP)
[(100  5)/1140] = [(100  5)/x]
? x = (105 x 1140/95) = 1260
? New SP = Rs 1260
3. 

SP = Rs. 27.50, Profit = 10%.
So, CP = Rs. (100/110 x 27.50) = 25
When SP = Rs 25.75, Profit = (25.75  25) = 0.75
∴ Profit % = (0.75/25 x 100)% = 3%
4. 

Let CP of each article be Rs 1
Then, CP of 18 article = Rs 18,
SP of 18 articles = Rs 21
∴ Gain % = (3/18 x 100)% = 16 + (2/3)%
5. 

Then, (SP of 33 m)  (CP of 33 m)
Gain = SP of 11 m
∴ Let CP of each metre be Re 1
Then CP of 22 m = Rs 22,
SP of 22 m = Rs 33
∴ Gain % = (11/22 x 100)% = 50%
6. 

Suppose, Number of bananas bought = LCM of 6 and 4 = 12
⇒CP = Rs (10/2 x 12) = Rs 20
SP = Rs (6/4 x 12) = Rs 18
⇒ Loss % = (2/20 x 100) = 10%
7. 

CP of 200 kg of mixture = Rs (80 x 13.80 + 120 x 16)
= Rs. 3000
SP = 116% of Rs 3000
= Rs (116/100 x 3000) = Rs 3480
∴ Rate of SP of the mixture = Rs (3480/200) per kg
= Rs 17.40 per kg
8. 

CP of 3 toffees = Rs 1
SP of 3 toffees = 150% of Rs 1 = 3/2
For Rs 3/2, toffees sold = 3 For Rs 1
toffees sold = (3 x 2/3) = 2
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