Answer

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**Hint:**In this question, we have to find the loss or gain percentage. For that we have to find whether the shopkeeper gets gain or loss. So let us first find out the total cost value for buying the tables. Then we will find the total selling price. With the help of it we will get the total loss or gain then we can find the required solution.

**Complete step-by-step answer:**

It is given that, in the furniture shop, \[24\]tables were bought at the rate of Rs \[450\] per table.

Also, the shopkeeper sold \[16\]of them at the rate of Rs\[600\] per table and the remaining at the rate of \[400\]per table.

We need to find out the loss or gain percentage.

Thus first we need to find out the total cost price.

The shopkeeper bought \[24\] tables at the rate of Rs \[450\] per table.

Therefore the total cost price =\[24 \times 450 = 10800\]

The shopkeeper sold \[16\]of them at the rate of Rs\[600\] per table and the remaining that is\[24 - 16 = 8\] at the rate of \[400\]per table. Thus the total selling price is = \[16 \times 600 + 8 \times 400 = 12800\]

Since the selling price is greater than the cost price we can say that the shopkeeper gets gain on selling these chairs.

Here gain is given by the formula, \[{\rm{gain = selling price - cost price}}\]

Total gain is =\[12800 - 10800 = 2000\]

We can gain percentage using the formula

\[{\rm{gain}}\% = \dfrac{{{\rm{gain}}}}{{CP}} \times 100\]

Therefore the gain % =\[\dfrac{{2000}}{{10800}} \times 100 = 18.51\% \]

**Hence the gain percent of the shopkeeper is \[18.51\% \]**

**Note:**If the cost price is greater than the selling price then we can say that there is a loss for the shopkeeper and the amount of loss found using the formula\[{\rm{ loss = CP - SP}}\].

Also while finding the gain percentage the gain amount must be placed in the numerator. We can also find the gain percentage by following method,

\[{\rm{gain\% = }}\dfrac{{12800}}{{10800}} \times 100 - 100\]

We get \[{\rm{ gain\% = 118}}{\rm{.51 - 100}}\]

That is \({\rm{gain \% = 18}}{\rm{.51\% }}\)

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