Short cuts for solving Profit and Loss problems  Vikas Saini

Q. By selling 18 oranges profit is equal to sp of 3 oranges.Find profit percentage.
Alternate approach:
Sp of 1 orange = x.
cp of 1 orange = y.
18x – 18y = 3x
= > 18 y = 15 x.
Profit percentage = (3x/18y)x100
= (3x/15x)x100
= 20%.
Short approach :
Profit percentage = [profit (quantity) / (Total quantity – profit)] x 100 = [(3)/(183)] x 100
= [3/15] x 100
= 20%
Q. By selling 18 chocolates,vendor loss selling price of 2 chocolates.Find loss percentage.
Alternative approach :
sp of 1 chocolate = x
cp of 1 chocolate = y
18 y – 18 x = 2x.
18 y = 20 x.
Loss percentage = (2x/18 y) x 100
= (2x/20x)x100
= 10%.
Short approach :
Loss percentage = [Loss (quantity) / (Total quantity + loss) ] x 100 = [ 2 / (18+2) ] x 100
= 10%.
Q. On selling an article for rs 576 a trader losses 4%.In order to gain 25/6 % , he must sell article for
A.6 55 rs B.676 rs C.625 rs D. 600 rs.
Alternate approach :
Cost price = [576 / (100 – 4)] x 100 = 600 rs.
Selling price = 600 x (1 + 25/(6 x 100) = 625.
Short approach :
Direct formula to find sp in such problems
= previous selling price x 100 x (1+ gain percent)/(1 – loss percent)
= 576 x 100 x (1+25/600)/(1 – 4/100)
= 625 rs.
Q. A goldsmith has 361 rings of gold.He sells some of them at a loss of 4% and rest at a profit of 15%. Overall profit is 8%.Find no of rings sold at profit of 15%.
Alternate approach :
Suppose he sold x no of rings at profit of 15%.
(361x)x(14/100)+x (1+15/100) = 361 x (1+8/100)
361 x 0.96 – 0.96x + 1.15x = 361x1.08
0.19 x = 361(1.080.96)
X = 361 x (0.12) / (0.19) = 228.
Short approach :
By allegation
4 15
8
7 12
No of rings = [(12)/(12+7)]x361 = 228.
Q. On selling 17 balls at rs 720,there is loss equal to the cost price of 5 balls.The cost price of a ball is
A. 45 rs B.50rs C.55rs D.60 rs.
Short approach :
Cp of ball = selling price of all balls / (total balls – loss(no of balls) = 720 / (175 )
= 60 rs.
Q. The cost price of 10 pens is the same as the selling price of n pens.If there is a loss of 40%.Find value of n.
Short approach :
n / n + 10 = 40/100
n = 6.66.
Q. A shopkeeper uses a weight of of 460 gm instead of 500 gm and sells the article at the cost price.What is profit percentage ?
A.40% B.23% C.8 +16/23 % D.20%
Short approach :
Profit percentage = [ (500 – 460)/460] x 100
= (40/460)x100