Average price across mixed purchases: Roshan buys 5 pants at ₹25 each, 10 shirts at ₹50 each, and 15 ties at ₹35 each. Compute the overall average price per article for all 30 items purchased.
Correct Answer: ₹ 38.33
Introduction / Context:This problem checks weighted average with unequal counts at different prices. We combine total cost over all items and divide by the total number of articles to obtain a single per-article average.
Given Data / Assumptions:
- Pants: 5 pieces at ₹25 each
- Shirts: 10 pieces at ₹50 each
- Ties: 15 pieces at ₹35 each
- Total number of articles = 5 + 10 + 15 = 30
Concept / Approach:Average price per article = total expenditure / total number of articles. Since quantities differ by item type, compute each subtotal and add them before dividing by 30.
Step-by-Step Solution:
Cost of pants = 5 * 25 = ₹125Cost of shirts = 10 * 50 = ₹500Cost of ties = 15 * 35 = ₹525Total cost = 125 + 500 + 525 = ₹1150Average price = 1150 / 30 = ₹38.333… ≈ ₹38.33Verification / Alternative check:Use a calculator to confirm 1150 divided by 30. Rounding to two decimals yields ₹38.33, which is consistent with currency presentation.
Why Other Options Are Wrong:
- ₹45.33, ₹42.00, ₹40.00, ₹45.00: do not equal the precise ratio of total cost to item count (1150/30).
Common Pitfalls:Adding the three prices and dividing by 3 ignores the different quantities. Always weight by quantity purchased.
Final Answer:₹ 38.33