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

Concept

When two item types share a known total quantity and a known total cost, set up two linear equations — one for quantity (sum of counts) and one for value (price per unit times count) — and solve them simultaneously to recover each count. Then apply each profit rate to the cost of the relevant share: Selling Price = Cost × (1 + profit fraction).

Application

For Shop B the table gives a total of 47 pencils and a total cost of Rs 415, with wooden pencils costing Rs 5 each and mechanical pencils Rs 20 each. Let w be the number of wooden pencils and m the number of mechanical pencils:

1. Quantity equation: w + m = 47.

2. Value equation: 5w + 20m = 415.

3. From the first equation w = 47 − m; substitute into the second: 5(47 − m) + 20m = 415, i.e. 235 + 15m = 415.

4. So 15m = 180, giving m = 12 and therefore w = 47 − 12 = 35 wooden pencils.

5. Split the 35 wooden pencils: 20% of 35 = 7 pencils sold at 20% profit; the remaining 35 − 7 = 28 pencils sold at 50% profit.

6. Selling price = 7 × 5 × 1.20 + 28 × 5 × 1.50 = 42 + 210 = 252.

Hence the total selling price of the wooden pencils is Rs 252.

Cross-check

Verify the counts against the cost data: 5 × 35 + 20 × 12 = 175 + 240 = 415, which matches the table exactly. The cost of the wooden stock is 35 × 5 = Rs 175, so a total selling price of Rs 252 means an overall profit of Rs 77 on the wooden pencils — consistent with a blend of 20% and 50% margins.