Question

a shopkeeper buys a dress for rs. 360 and puts a price tag on it to earn 30% profit. later he offered a discount of 12 raised to the power 1/2 % on the marked price. what percentage profit did he make.

Answer 1

Concept:

The profit is made when the Cost Price is lesser than Selling Price.

Profit percentage $=\frac{Profit*100}{C.P.}$

where C.P. is the cost price of the item.

Given:

The cost price (C.P.) of the dress $=Rs. 360.$

The profit earned by the price tag $=30$%.

Discount given on the marked price$=12\frac{1}{2}$%.

Find:

The profit percentage the shopkeeper made.

Solution:

Calculate 30% of the Cost Price (C.P.)

$\frac{30}{100} *360=108$

∴ $Profit= Rs. 108$

Selling Price = Cost Price + Profit

Selling Price (S.P.) $=360+108$

Selling Price (S.P.) $=468.$

∴ Price tag $= Rs. 468$

Calculate the discount of $12\frac{1}{2}$% on the Price tag

$12\frac{1}{2} =\frac{25}{2}$

$Discount=12.5$% on the price tag.

$\frac{12.5}{100}*468\\=Rs. 58.5$

Selling Price (S.P.) = Price tag - Discount

$S.P.=468-58.5\\S.P.=Rs.409.5$

∴ Selling Price $= Rs. 409.5$.

$Profit=S.P.-C.P.$

$Profit=409.5-360$

$Profit= Rs.49.5.$

Profit percentage $=\frac{Profit*100}{C.P.}$

$=\frac{49.5*100}{360}$

$=\frac{4950}{360}$

$=13.75$%

Hence the shopkeeper made a profit of $13.75$%.

∴ Option A, 13.75% is the correct answer.