Directions : Raghav bought some chairs & tables from a shopkeeper. The marked price of a chair and a table were in the ratio 5:7. The shopkeeper gives discounts of 20% and 25% on the chair & the table respectively. The ratio of chairs and tables bought by Raghav is 9:8.
If Raghav buys 170 chairs and tables in all, then what is the approximately average price at which he must sell all of them to be in a situation of no profit -no loss?

Options

A. Rs 458.8
B. Rs 526.7
C. Rs 488.8
D. Rs 428.8

Answer

To solve the problem step by step, we will follow the given data and perform the necessary calculations.

### Step 1: Understand the Ratios and Discounts
- The marked price of a chair (MP_chair) and a table (MP_table) are in the ratio of 5:7.
- Let the marked price of a chair be 5x and the marked price of a table be 7x.
- Discounts on the chair and table are 20% and 25%, respectively.

### Step 2: Calculate Selling Prices
- Selling Price of Chair (SP_chair):
\[ SP_{chair} = MP_{chair} - (20\% \text{ of } MP_{chair}) = 5x - 0.2(5x) = 5x - x = 4x \]

- Selling Price of Table (SP_table):
\[ SP_{table} = MP_{table} - (25\% \text{ of } MP_{table}) = 7x - 0.25(7x) = 7x - 1.75x = 5.25x \]

### Step 3: Determine the Number of Chairs and Tables
- The ratio of chairs to tables bought by Raghav is 9:8.
- Let the number of chairs be 9k and the number of tables be 8k.
- The total number of chairs and tables is given as 170:
\[ 9k + 8k = 170 \implies 17k = 170 \implies k = 10 \]
- Therefore, the number of chairs is:
\[ 9k = 9 \times 10 = 90 \text{ chairs} \]
- And the number of tables is:
\[ 8k = 8 \times 10 = 80 \text{ tables} \]

### Step 4: Calculate Total Cost Price
- Total Cost Price (CP) for chairs:
\[ CP_{chairs} = \text{Number of chairs} \times SP_{chair} = 90 \times 4x = 360x \]
- Total Cost Price for tables:
\[ CP_{tables} = \text{Number of tables} \times SP_{table} = 80 \times 5.25x = 420x \]

- Total Cost Price:
\[ CP_{total} = CP_{chairs} + CP_{tables} = 360x + 420x = 780x \]

### Step 5: Calculate Total Selling Price
- Total Selling Price (SP) for all items:
\[ SP_{total} = \text{Number of chairs} \times SP_{chair} + \text{Number of tables} \times SP_{table} = 90 \times 4x + 80 \times 5.25x \]
\[ SP_{total} = 360x + 420x = 780x \]

### Step 6: Calculate Average Selling Price
- Average Selling Price (ASP) to achieve no profit, no loss:
\[ ASP = \frac{SP_{total}}{\text{Total number of items}} = \frac{780x}{170} \]

### Step 7: Calculate the Value of x
- Since we need the average price, we can assume a value for x to simplify calculations. Let’s assume x = 100 (this is arbitrary but simplifies calculations):
\[ ASP = \frac{780 \times 100}{170} = \frac{78000}{170} \approx 458.82 \]

### Conclusion
Thus, the average price at which Raghav must sell all of them to be in a situation of no profit, no loss is approximately **Rs. 458.8**.