Question

retailer marks the price of a shirt at 16% more than the cost price.He then gave a discount of 12% on the marked price.Find the loss% and gain%​

Answer 1

Given :-

A retailer marks the price of a shirt at 16% more than the cost price.

He gave a discount of 12% on the marked price.

To find :-

The percentage of loss or gain .

Solution :-

Let the Cost Price of the shirt be Rs. X

The Marked Price of the shirt

= 16% more than the cost price

= Cost Price + 16% of the Cost Price

= X + (16% of X)

= X + (16% × X)

= X + [16/100)×X]

= X + [(4/25)×X]

= X+ [(4×X)/25]

= X+(4X/25)

= (25X+4X)/25

= 29X/25

The Marked Price of the shirt

= Rs. 29X/25

Given discount on it = 12%

Discount = 12% of the Marked Price

=> Discount = 12% of 29X/25

=> Discount = (12/100)×(29X/25)

=> Discount = (3/25)×(29X/25)

=> Discount = (3×29X)/(25×25)

=> Discount = 87X/625

Discount = Rs. 87X/625

Selling Price = Marked Price - Discount

=> Selling Price = (29X/25)-(87X/625)

LCM of 25 and 625 = 625

=> Selling Price = (725X-87X)/625

=> Selling Price = 638X/625

The Selling Price of the shirt = Rs. 638X/625

Selling Price > Cost Price

Gain occurs

Gain = Selling Price - Cost Price

=> Gain = (638X/625)-X

=> Gain = (638X-625X)/625

=> Gain = Rs. 13X/625

We know that

Gain % = (Gain /Cost Price)×100

=> G% = [(13X/625)/X]×100

=> G% = (13X/625X)×100

=> G% = (13/625)×100

=> G% = (13×100)/625

=> G% = 1300/625

=> G % = 52/25

=> G % = 2 2/25

=> G% = 2.08

Answer :-

The Gain percentage on it is 52/25% or

2 2/25 % or 2.08%

Used formulae:-

♦ Selling Price = Marked Price - Discount

♦ Gain = Selling Price - Cost Price

♦ Gain % = (Gain /Cost Price)×100

Answer 2

PROVIDED INFORMATION :-

• retailer marks the price of a shirt at 16% more than the cost price

• He then gave a discount of 12% on the marked price

TO CALCULATE :-

• Find the loss% and gain% = ?

CONCEPT USED :-

• Formula to find SP = MP - D

• formula to find gain = SP - CP

• formula to find gain = (gain/cost price)×100

UNDERSTANDING CONCEPT :-

Cost Price (C.P.):-

Price at which an article is purchased

Selling Price (S.P.):-

Price at which an article is sold by a shopkeeper.

If the selling price is more than the cost price then it is known as

profit.

Profit = Selling price - Cost price

If the selling price is less than the cost price then it is known as loss.

Profit percentage is calculated on cost price.

Loss percentage is calculated on cost price.

Loss % = Loss/Cost Price × 100

SOLUTION :-

Let Cost price in 100 Rupees

so mark price = 116 Rupees

we know ,

SP = 100 - D%/100 × MP

SP = 100 - 12 /100 × 116

SP = 88/100 × 116

SP = 102.08 Rupees

here C.P = 100

Profit = 102.08 - 100

= 2.08 Rupees

gain % = 2.08/100 × 100

= 2.08%

loss% and gain% = 2.08%

ADDITIONAL INFORMATION :-

• This question is a formula based question. The main step of this question is to calculate the selling price separately and finally add them. In this way we can calculate gain or loss in the whole transaction.

• For profit, the selling price should be more than the cost price while for loss, cost price should be more than the selling price.