Read the given data carefully and answer the following question.

There are a total of 1080 bags (fabric + paper) sold by shops A, B, and C.

(i) Shop A sold 25\% more bags (paper + fabric) than shop B. The number of paper and fabric bags sold by shop B are equal.

(ii) The number of paper bags sold by shop B is twice the number of fabric bags sold by shop A.

(iii) The number of paper bags sold by shop C is 50\% of the fabric bags sold by shop A.

(iv) The number of fabric bags sold by shop C is 25\% of the fabric bags sold by shop B.

**Question:** Fabric bags sold by shop A are what percentage more than paper bags sold by shop C?

Question

Read the given data carefully and answer the following question.

There are a total of 1080 bags (fabric + paper) sold by shops A, B, and C.

(i) Shop A sold 25\% more bags (paper + fabric) than shop B. The number of paper and fabric bags sold by shop B are equal.

(ii) The number of paper bags sold by shop B is twice the number of fabric bags sold by shop A.

(iii) The number of paper bags sold by shop C is 50\% of the fabric bags sold by shop A.

(iv) The number of fabric bags sold by shop C is 25\% of the fabric bags sold by shop B.

**Question:** Fabric bags sold by shop A are what percentage more than paper bags sold by shop C?

Accepted Answer

**Solution:**

1. Let the number of bags sold by shop B be $x$. Since shop A sold 25\% more than shop B, bags sold by shop A = $1.25x$.

2. Total bags sold by A, B, and C = 1080, so bags sold by C = $1080 - (x + 1.25x) = 1080 - 2.25x$.

3. Given that shop B sold equal number of paper and fabric bags, so paper bags by B = fabric bags by B = $\frac{x}{2}$.

4. Paper bags sold by B = twice fabric bags sold by A:
   $$
   \frac{x}{2} = 2 \times \text{fabric bags by A} \implies \text{fabric bags by A} = \frac{x}{4}
   $$

5. Total bags sold by A = paper bags by A + fabric bags by A = $1.25x$.
   So, paper bags by A = $1.25x - \frac{x}{4} = \frac{5x}{4} - \frac{x}{4} = \frac{4x}{4} = x$.

6. Paper bags by C = 50\% of fabric bags by A = $0.5 \times \frac{x}{4} = \frac{x}{8}$.

7. Fabric bags by C = 25\% of fabric bags by B = $0.25 \times \frac{x}{2} = \frac{x}{8}$.

8. Total bags by C = paper + fabric = $\frac{x}{8} + \frac{x}{8} = \frac{x}{4}$.

9. From step 2, $1080 - 2.25x = \frac{x}{4} \implies 1080 = 2.25x + \frac{x}{4} = \frac{9x}{4} + \frac{x}{4} = \frac{10x}{4} = 2.5x$.

10. Solve for $x$:
    $$
    2.5x = 1080 \implies x = \frac{1080}{2.5} = 432
    $$

11. Fabric bags by A = $\frac{x}{4} = \frac{432}{4} = 108$.

12. Paper bags by C = $\frac{x}{8} = \frac{432}{8} = 54$.

13. Required percentage increase:
    $$
    \frac{\text{Fabric bags by A} - \text{Paper bags by C}}{\text{Paper bags by C}} \times 100 = \frac{108 - 54}{54} \times 100 = \frac{54}{54} \times 100 = 100\% 
    $$

**Answer:** 100\%

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