Read the given data carefully and answer the following question. A total of…

Concept

Concept: To compare the averages of two groups taken over the same set of items (here, 3 shops), the difference of the averages equals the difference of the totals divided by the number of items: |average(paper) - average(fabric)| = |total(paper) - total(fabric)| / 3. So we first build the full shop-wise table of paper and fabric counts from the given conditions, then take totals.

Application

1. Let the number of fabric bags sold by shop A be x. From condition (iii), paper bags of B = 2x, and from condition (ii), fabric of B = paper of B = 2x.

2. From condition (i), A's total = 25% more than B's total = 1.25 x (2x + 2x) = 5x. Since A's fabric = x, A's paper = 5x - x = 4x.

3. From condition (iv), paper of C = 50% of A's fabric = 0.5x. From condition (v), fabric of C = 25% of B's fabric = 0.25 x 2x = 0.5x.

4. Sum of all six counts = 4x + x + 2x + 2x + 0.5x + 0.5x = 10x = 1080, so x = 108.

5. Paper total = 4x + 2x + 0.5x = 6.5x = 702; Fabric total = x + 2x + 0.5x = 3.5x = 378.

6. Difference of averages = |702 - 378| / 3 = 324 / 3 = 108.

Shop-wise distribution

Cross-check: All counts come out as whole numbers (A: 432 paper, 108 fabric; B: 216 paper, 216 fabric; C: 54 paper, 54 fabric), they sum to 1080, and every condition holds, confirming the result.