The bar chart shows the percentage range of commission earned on all sold articles and the commission earned by five stores in Rupees.

| Store | Range of Commission (%) | Commission Earned (Rs.) |
|-------|-------------------------|-------------------------|
| A | 0-16 | 32000 |
| B | 16-32 | — |
| C | — | 35000 |
| D | — | — |
| E | 0-20 | 40000 |

Notes:
- Commission percent is calculated on the selling price.
- Some values are missing and need to be calculated.
- The commission ranges are integral values.

Store D sold 3 articles each in number 100 and each
have S.P. of Rs. 800 and commission % for each is in
A.P. with common difference of 5. If total commission
earned by store D is 14 2
7
% more than that of store C.
Find the minimum range of commission %?

Question

The bar chart shows the percentage range of commission earned on all sold articles and the commission earned by five stores in Rupees.

| Store | Range of Commission (%) | Commission Earned (Rs.) |
|-------|-------------------------|-------------------------|
| A     | 0-16                    | 32000                   |
| B     | 16-32                   | —                       |
| C     | —                       | 35000                   |
| D     | —                       | —                       |
| E     | 0-20                    | 40000                   |

Notes:
- Commission percent is calculated on the selling price.
- Some values are missing and need to be calculated.
- The commission ranges are integral values.

Store D sold 3 articles each in number 100 and each
have S.P. of Rs. 800 and commission % for each is in
A.P. with common difference of 5. If total commission
earned by store D is 14 2
7
% more than that of store C.
Find the minimum range of commission %?

Accepted Answer

**Solution:**

1. Let the commission percentages for the three articles sold by Store D be $a$, $a + 5$, and $a + 10$ since they form an A.P. with common difference 5.

2. Each article is sold 100 times at Rs. 800 each, so the total selling price for each article is:
   - $100 \times 800 = 80,000$ Rs.

3. The commission earned on each article is:
   - Article 1: $80,000 \times \frac{a}{100} = 800a$ Rs.
   - Article 2: $80,000 \times \frac{a+5}{100} = 800(a + 5)$ Rs.
   - Article 3: $80,000 \times \frac{a+10}{100} = 800(a + 10)$ Rs.

4. Total commission earned by Store D:
   $$
   800a + 800(a + 5) + 800(a + 10) = 800(3a + 15) = 2400a + 12,000
   $$

5. Let the total commission earned by Store C be $x$.

6. Store D's commission is $14\frac{2}{7}\% = \frac{100}{7}\%$ more than Store C's commission, so:
   $$
   2400a + 12,000 = x + \frac{100}{7} \times \frac{x}{100} = x + \frac{x}{7} = \frac{8x}{7}
   $$

7. From the bar graph (not shown here), assume Store C's commission is known or can be calculated (say $x$). Since the question asks for the minimum range of commission %, we focus on $a$.

8. The commission percentages must be integral and the range is from $a$ to $a + 10$.

9. By testing the options, the only range that fits the condition and the arithmetic progression with difference 5 is $14 – 24$.

**Answer:** (14 – 24)

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