Directions : Abhishek bought some chairs and tables from a shopkeeper. The marked price of a chair and a table were in the ratio 5:8. The shopkeeper gave discounts of 20% and 25% on the chair & 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 Rs.300 more than that of a chair and the total expenditure made by Abhishek in purchasing the chairs and tables from the shopkeeper was Rs108000, then how many chairs were purchased by Abhishek?

Options

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

Answer

To solve the problem step by step, we will follow the information provided in the question and systematically calculate the required values.

### Step 1: Define the Marked Prices
Let the marked price of a chair be \(5x\) and the marked price of a table be \(8x\), based on the given ratio of 5:8.

### Step 2: Determine the Difference in Marked Prices
According to the problem, the marked price of the table is Rs. 300 more than that of the chair. Therefore, we can set up the equation:
\[ 8x = 5x + 300 \]
Solving for \(x\):
\[ 8x - 5x = 300 \implies 3x = 300 \implies x = 100 \]

### Step 3: Calculate the Marked Prices
Now we can find the marked prices:
- Marked price of a chair = \(5x = 5 \times 100 = Rs. 500\)
- Marked price of a table = \(8x = 8 \times 100 = Rs. 800\)

### Step 4: Calculate the Selling Prices after Discounts
The shopkeeper gives discounts of 20% on chairs and 25% on tables.
- Selling price of a chair:
\[ \text{Selling Price of Chair} = 500 - (20\% \text{ of } 500) = 500 - 100 = Rs. 400 \]
- Selling price of a table:
\[ \text{Selling Price of Table} = 800 - (25\% \text{ of } 800) = 800 - 200 = Rs. 600 \]

### Step 5: Set Up the Ratio of Quantities
Let the number of chairs purchased be \(6y\) and the number of tables purchased be \(5y\) (as given in the ratio of 6:5).

### Step 6: Write the Total Expenditure Equation
The total expenditure made by Abhishek is given as Rs. 108000. Therefore, we can write:
\[ \text{Total Cost} = (\text{Number of Chairs} \times \text{Selling Price of Chair}) + (\text{Number of Tables} \times \text{Selling Price of Table}) \]
Substituting the values:
\[ 108000 = (6y \times 400) + (5y \times 600) \]

### Step 7: Simplify the Equation
\[ 108000 = 2400y + 3000y \]
\[ 108000 = 5400y \]

### Step 8: Solve for \(y\)
\[ y = \frac{108000}{5400} = 20 \]

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

### Conclusion
Abhishek purchased **120 chairs**.

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