Inventory ratio and mean: In a stationery shop, the ratio of pens to pencils is 3 : 2, and the average of the two counts is 180 (i.e., (pens + pencils) / 2 = 180). What is 30% of the number of pencils?

Introduction / Context:The phrase “average of the two counts is 180” means (pens + pencils)/2 = 180. With the ratio of 3 : 2, we can find each count and then compute 30% of the pencil count (which may be fractional if not an integer multiple of 10).

Given Data / Assumptions:

• Pens : Pencils = 3 : 2
• (Pens + Pencils) / 2 = 180 ⇒ Pens + Pencils = 360

Concept / Approach:Let pens = 3k and pencils = 2k. Then 5k = 360 → k = 72. Thus pencils = 2k = 144. Compute 30% of 144 as 0.30 * 144.

Step-by-Step Solution:

Verification / Alternative check:Pens = 3k = 216. Check average: (216 + 144)/2 = 360/2 = 180, consistent with the prompt.

Why Other Options Are Wrong:

• 144, 72, 57.6, 86.4: these are counts or other percentages, not exactly 30% of 144.

Common Pitfalls:Misreading “average” as 180 each or misapplying the ratio to the average rather than to the actual counts.

Final Answer:43.2