The table given below shows the total number of wooden and mechanical pencils…

Concept

In this table each shop lists the TOTAL number of pencils (wooden + mechanical) and the TOTAL price of those pencils. With a fixed unit price for each kind (wooden = Rs 5, mechanical = Rs 20), the two figures give two linear equations per shop, so the split can be recovered uniquely.

Let w = wooden count and m = mechanical count in a shop. Then w + m = total count and 5w + 20m = total price. Subtracting 5 times the first equation from the second isolates the mechanical pencils:

5w + 20m = price, and 5w + 5m = 5 x (total count); subtracting gives 15m = price - 5 x (total count), so m = (price - 5 x total) / 15, and w = total - m.

Application

Compute the mechanical count for A and B, and the wooden count for D, then convert each to cost (mechanical x Rs 20, wooden x Rs 5).

1. Shop A: m = (490 - 5 x 38) / 15 = (490 - 190) / 15 = 300 / 15 = 20 mechanical pencils.

2. Shop B: m = (415 - 5 x 47) / 15 = (415 - 235) / 15 = 180 / 15 = 12 mechanical pencils.

3. Mechanical pencils in A and B together = 20 + 12 = 32, so their cost = 32 x 20 = Rs 640.

4. Shop D: m = (900 - 5 x 75) / 15 = (900 - 375) / 15 = 525 / 15 = 35 mechanical pencils, so wooden = 75 - 35 = 40.

5. Cost of wooden pencils in D = 40 x 5 = Rs 200.

6. Required ratio = 640 : 200 = 16 : 5 (dividing both by 40).

Cross-check

Verify the counts satisfy the original totals for each shop used:

All counts are whole numbers and reproduce the given totals and prices, so the ratio 16 : 5 is confirmed.