The table given below shows the total number of wooden and mechanical pencils…
2025
The table given below shows the total number of wooden and mechanical pencils in five shops and it also shows the price of total mechanical and wooden pencils.
Find the total mechanical pencil in C is what percentage of total wooden pencil in E.
Answer: B. 200 — Concept: When a group of N items of two kinds has a known total count and a known total value, and each kind has a fixed unit price, the count of each kind is…
- A.
100
- B.
200
- C.
160
- D.
150
- E.
102
Attempted by 18 students.
Show answer & explanation
Correct answer: B
Concept:
When a group of N items of two kinds has a known total count and a known total value, and each kind has a fixed unit price, the count of each kind is found by solving two linear equations in two unknowns: (count1 + count2 = total count) and (price1·count1 + price2·count2 = total value). 'A is what percent of B' is then (A / B) × 100.
Application — Shop C (find mechanical pencils):
Let w = wooden and m = mechanical pencils in C. Total count: w + m = 112.
Total value at Rs 5 (wooden) and Rs 20 (mechanical): 5w + 20m = 1310.
Multiply the count equation by 5: 5w + 5m = 560.
Subtract from the value equation: (5w + 20m) − (5w + 5m) = 1310 − 560, i.e. 15m = 750, so m = 50. Mechanical pencils in C = 50.
Application — Shop E (find wooden pencils):
Let w = wooden and m = mechanical pencils in E. Total count: w + m = 40.
Total value: 5w + 20m = 425.
Multiply the count equation by 5: 5w + 5m = 200.
Subtract from the value equation: 15m = 225, so m = 15, and w = 40 − 15 = 25. Wooden pencils in E = 25.
Result: Mechanical in C as a percent of wooden in E = (50 ÷ 25) × 100 = 200%.
Cross-check: Put the values back. Shop C: 62 wooden × 5 + 50 mechanical × 20 = 310 + 1000 = 1310 ✓ (62 + 50 = 112 ✓). Shop E: 25 wooden × 5 + 15 mechanical × 20 = 125 + 300 = 425 ✓ (25 + 15 = 40 ✓). Both totals match, so 50 and 25 are confirmed and the ratio gives 200%.