Question

a retailer gives a discount of 20% and yet earns a profit of 10% what is the ratio of cost price to the list price​

Answer 1

CONCEPT:

Selling Price, Cost Price, and Marked Price Concept

GIVEN:

Profit % = 10%

Discount % = 20%

FIND:

The ratio of Cost Price and Marked Price

SOLUTION:

Let the Cost Price of the product is x

The Selling Price of the product will be = Cost Price * (100 + Profit %) / 100

= x * (100+10) / 100

= 110x / 100

= 11x / 10 _________ (1)

Also, there is a discount of 20% on the Product

So,

The Selling Price of the product will be = Marked Price * (100 - Discount %) / 100

= M.P * (100-20) / 100

= M.P * (8/10)

Therefore,

M.P = (11x / 10) * ( 100 / 80 ) ________ ( From 1 )

= ( 11 x / 8 ) ________ (2)

Now, the ratio of Cost Price to the Marked Price is:

= x / (11x / 8)

= 8 : 11

Hence, the ratio of Cost Price to List Price is 8:11.

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Answer 2

Answer:

8:11

Step-by-step explanation:

Given,

A retailer gives a discount of 20% and yet earns a profit of 10%.

To Find,

The ratio of cost price to the list price.

So,

Let the Cost Price of the product be x.

Using the formula:

Selling Price of the product = $Cost Price\frac{100 + profit percent}{100}$

= $x\frac{100 +10}{100}$

= $\frac{110x}{100}$

= $\frac{11x}{10}$

As mentioned,

There is a discount of 20% on the Product.

So,

The Selling Price of the product will be = $Marked Price\frac{100 - discount percent}{100}$

= $Marked Price\frac{100 - 20}{100}$

= $Marked Price\frac{80}{100}$

= $Marked Price\frac{8}{10}$

Therefore,

Marked Price = $\frac{11x}{10}X\frac{100}{80}$

                      = $\frac{11x}{8}$

Now,

The ratio of Cost Price to the Marked Price is:

= $\frac{x}{\frac{11x}{8} }$

= 8 : 11

Hence, 8:11 is the correct answer.

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