Read the following information carefully and answer given question below:
Abhishek bought some chairs and tables from a shopkeeper. The prices of a chair and table were in the ratio of 5:8. The shopkeeper have discounts of `20%` and `25%` on the chair and the table respectively. The ratio of number of chairs and tables bought by Abhishek is 6:5.
If the marked price of a table set by the shopkeeper was Rs300 more than that of a chair and the total expenditure made by Abhishek in purchasing the chair and table from the shopkeeper was Rs108000, then how many chair were purchased by Abhishek?

Options

A. 150
B. 60
C. 120
D. 90

Answer

To solve the problem step by step, we will break down the information given and perform the necessary calculations.

### Step 1: Define Variables
Let the price of a chair be \(5x\) and the price of a table be \(8x\) (since the ratio of the prices is 5:8).

### Step 2: Establish the Relationship Between Prices
According to the problem, the marked price of a table is Rs 300 more than that of a chair. Therefore, we can write:
\[ 8x = 5x + 300 \]

### Step 3: Solve for \(x\)
Rearranging the equation gives:
\[ 8x - 5x = 300 \implies 3x = 300 \implies x = 100 \]

### Step 4: Calculate the Prices of Chair and Table
Now that we have \(x\), we can find the prices:
- Price of a chair = \(5x = 5 \times 100 = 500\)
- Price of a table = \(8x = 8 \times 100 = 800\)

### Step 5: Calculate Selling Prices After Discounts
Next, we apply the discounts:
- Discount on chair = 20% of 500 = \(0.2 \times 500 = 100\)
- Selling price of chair = \(500 - 100 = 400\)

- Discount on table = 25% of 800 = \(0.25 \times 800 = 200\)
- Selling price of table = \(800 - 200 = 600\)

### Step 6: Define the Number of Chairs and Tables
Let the number of chairs purchased be \(6y\) and the number of tables purchased be \(5y\) (since the ratio of chairs to tables is 6:5).

### Step 7: Calculate Total Expenditure
The total expenditure can be expressed as:
\[ \text{Total Expenditure} = (\text{Number of Chairs} \times \text{Selling Price of Chair}) + (\text{Number of Tables} \times \text{Selling Price of Table}) \]
Substituting the values we have:
\[ 108000 = (6y \times 400) + (5y \times 600) \]
\[ 108000 = 2400y + 3000y \]
\[ 108000 = 5400y \]

### Step 8: Solve for \(y\)
Now, we can solve for \(y\):
\[ y = \frac{108000}{5400} = 20 \]

### Step 9: Calculate the Number of Chairs Purchased
Finally, the number of chairs purchased is:
\[ \text{Number of Chairs} = 6y = 6 \times 20 = 120 \]

### Final Answer
Abhishek purchased **120 chairs**.

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