If a man bought 9 sharpeners for ₹4, and sold them at 5 sharpeners for ₹8, then the gain percentage is

Bihar NHM CHO-2025

Non Nursing Subjects

Hard

Appeared in: Bihar NHM CHO-2025

Explanation

To compare cost and selling prices, a common quantity of items must be used. The Least Common Multiple (LCM) of 9 and 5 is 45.
The cost price (CP) for 45 sharpeners is calculated as (₹4 / 9 sharpeners) × 45 sharpeners = ₹20.
The selling price (SP) for 45 sharpeners is calculated as (₹8 / 5 sharpeners) × 45 sharpeners = ₹72.
The total gain is the difference between the selling price and cost price: Gain = SP - CP = ₹72 - ₹20 = ₹52.
The gain percentage is calculated using the formula (Gain / CP) × 100, which is (₹52 / ₹20) × 100 = 260%.

Option A: A gain of 280% on a cost price of ₹20 would mean a profit of ₹56 (2.8 × 20), leading to a selling price of ₹76. The calculated selling price is ₹72.
Option B: A gain of 250% on a cost price of ₹20 would mean a profit of ₹50 (2.5 × 20). The actual profit is ₹52.
Option C: A gain of 270% on a cost price of ₹20 would mean a profit of ₹54 (2.7 × 20). The actual profit is ₹52.

Visual 1: Flowchart: A visual flowchart illustrating the step-by-step process: 1. Find LCM of quantities → 2. Calculate total CP for LCM quantity → 3. Calculate total SP for LCM quantity → 4. Calculate Gain (SP - CP) → 5. Calculate Gain % [(Gain/CP) * 100].

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of gain percentage in a profit and loss problem where the quantity bought and sold are different as background academic context rather than a clinical decision trigger.
Understanding profit and loss calculations is a fundamental life skill for financial literacy, budgeting, and making informed purchasing decisions.
This concept is foundational for anyone involved in business, sales, or entrepreneurship, including managing finances for a small clinic or pharmacy.
What if the sharpeners were sold at a loss? If 45 sharpeners were sold for ₹15 instead of ₹72, the loss would be CP - SP = ₹20 - ₹15 = ₹5. The loss percentage would be (Loss / CP) × 100 = (5 / 20) × 100 = 25%.

How to Approach the Question

First, read the question carefully and identify the given information: the cost price for a certain quantity and the selling price for a different quantity.
Recognize that you cannot directly compare the prices because the quantities are different. The core task is to find the prices for an equal number of items.
Determine a common quantity by finding the Least Common Multiple (LCM) of the number of items bought (9) and sold (5). The LCM is 45.
Calculate the total cost price for this common quantity (45 sharpeners).
Calculate the total selling price for the same common quantity (45 sharpeners).
Use the standard formula for gain percentage: Gain % = [(Selling Price - Cost Price) / Cost Price] × 100.

Concept Tested & Keywords

Concept Tested: Calculation of gain percentage in a profit and loss problem where the quantity bought and sold are different.
Stem keywords: bought 9 sharpeners for ₹4, sold 5 sharpeners for ₹8, gain percentage
Lead-in keywords: the gain percentage is

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