Question

When a chair is sold at Rs. 450, the owner loses 10%. At what price must that chair is be sold in order to gain 20%?​

Answer 1

Step-by-step explanation:

Given When a chair is sold at Rs. 450, the owner loses 10%. At what price must that chair is be sold in order to gain 20%?

• So let the cost price be 100 m
• Now there is a loss of 10%
• So the selling price of the chair will be 100 m – 10% of 100 m
•                                                                   = 90 m
• According to the question
•              90 m = 450
•                  m = 450 / 90
•                    Or m = 5
• Therefore 100 x m = 100 x 5 = Rs 500
• So the cost price of the chair is Rs 500
• Now in order to gain 20%
• Selling price of the chair = 500 + 20% of 500
•                                            = 500 + 100
•                                              = Rs 600
• Therefore the selling price should be Rs 600

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Answer 2

The chair must be sold at Rs. 600 in order to gain 20%.

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Let's understand a few concepts:

What is the cost price?

The cost price is the original price of items or goods at which it is bought by the retailer.

What is the selling price?

The selling price is the price of items or goods at which it is sold to the customer.

What is profit?

A profit usually occurs in the transaction when the selling price of the item is more than the cost price of the item.

What is loss?

A loss usually occurs in the transaction when the cost price of the item is more than the selling price of the item.

How to calculate the cost price and selling price of an item?

We will use the following formula to calculate the C.P. & S.P.:

$\boxed{\bold{C.P. = \bigg(\frac{100}{100 - Loss\%} \bigg)\times S.P.}}$

$\boxed{\bold{S.P. = \bigg(\frac{100 + Gain\%}{100} \bigg)\times C.P.}}$

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Let's solve the given problem:

The S.P. of the chair = Rs. 450

The loss percentage earned = 10%

By using the above formula of C.P., we get,

The cost price of the chair is,

= $\bigg(\frac{100}{100 - 10} \bigg)\times 450$

= $\bigg(\frac{100}{90} \bigg)\times 450$

= $\bigg(\frac{10}{9} \bigg)\times 450$

= $10\times 50$

= $Rs.\:500$

Now, we have to find the S.P. of the chair if the owner wants to make a profit of 20% in the transaction, so, by using the above formula of S.P., we get

The S.P. of the chair must be,

= $\bigg(\frac{100 + 20}{100} \bigg)\times 500$

= $\bigg(\frac{120}{100} \bigg)\times 500$

= $\frac{6}{5}\times 500$

= $6\times 100$

= $\bold{Rs.\:600}$

Thus, the S.P. of the chair must be Rs. 600 to gain 20%.

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