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Shortcut 33:
Selling price at profit or loss

\(S.P=C.P\pm(a/100)C.P\)

Substitute ‘+’ if profit; ‘-‘ if loss
Question:
A product worth Rs. 25000 is sold at a profit of 35%. Find the selling price?
Answer:
a = +35
C.P = 25000
Substitute the values in the above equation, we get
S.P = 25000 + (35/100)25000
S.P = 33750
Selling price = Rs. 33750

Shortcut 34:

Successive profit or loss

\(S.P=\frac{100+a}{100}\times\frac{100+b}{100}\times\frac{100+c}{100}C.P\)

a, b , c = values of percentage profit or loss
Substitute ‘+’ for profit and ‘-‘ for loss
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
D bought the watch for Rs. 4410

Shortcut 35:

Steady profit or loss

\(S.P=C.P\lbrack1+(a/100)\rbrack^n\)

a = value of profit or loss
Substitute ‘+’ for profit and ‘-‘ for loss
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 36:
Discount percentage

\(D\%=\frac{M.P-S.P}{M.P}\times100\)

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%