Unitary method: If 12 pens cost ₹ 84, what is the cost of 10 such pens?
Aptitude
Unitary Method
Difficulty: Easy
Choose an option
Answer
Correct Answer: ₹ 70
Explanation
Introduction / Context:The unitary method helps convert a given bundle price to a per-item rate, then to the cost of another quantity. This is routine in direct proportion pricing problems.Given Data / Assumptions:
- 12 pens → ₹ 84 total.
- Find cost for 10 pens at the same unit rate.
Concept / Approach:Compute the unit price and scale by the desired count: cost = (total/quantity) × target quantity.Step-by-Step Solution:
Unit price = 84 / 12 = ₹ 7 per pen.Cost for 10 pens = 10 × 7 = ₹ 70.Verification / Alternative check:Proportional check: 10 is 5/6 of 12, so cost should be 5/6 of ₹ 84 → ₹ 70. This matches perfectly.Why Other Options Are Wrong:
- ₹ 72 or ₹ 90: These correspond to different counts at ₹ 7 each (e.g., 10.285… pens or nearly 13 pens), not 10.
- ₹ 65: Not consistent with the computed unit price.
Common Pitfalls:Rounding the unit price prematurely (e.g., calling it ₹ 7.1) or dividing the wrong way. Always verify the unit price first, then multiply.
Final Answer:
₹ 70