Question

At style cloth emporium the shopkeeper measures \(20 \%\) less for every metre of cloth also he marks-up goods by \(20 \%\). What is the profit percentage? (a) \(50 \%\) (b) \(80 \%\) (c) \(75 \%\) (d) none of these

Short answer

Answer: The profit percentage is 16%.

Step-by-step solution

Calculate the actual cost per meter of cloth

Let the original cost per meter of cloth be denoted as \(C\). If the shopkeeper measures 20% less for every meter, then the actual cost per meter becomes \(0.8C\), as he only paid for 80% of the meter. (\(20\%\) less than 100% is 80%)

Calculate the selling price per meter after the 20% mark-up

Now, the shopkeeper marks-up the goods he buys by 20%. We will calculate the selling price per meter considering the mark-up. If the actual cost per meter is \(0.8C\) and he marks-up the goods by 20%, then the selling price per meter (let's denote it as \(S\)), can be calculated as: \(S = 0.8C*(1 + 0.2) = 0.8C * 1.2\).

Calculate the profit per meter

To calculate the profit (\(P\)) per meter, we need to subtract the cost price per meter from the selling price per meter: \(P = S - 0.8C\). Substituting the value of \(S\) from Step 2: \(P = (0.8C * 1.2) - 0.8C\) Now distribute \(0.8C\): \(P = 0.96C - 0.8C\)

Simplify the profit per meter

Subtracting the two values gives: \(P = 0.16C\). This is the profit per meter.

Calculate the profit percentage

To find the profit percentage, we will need to divide the profit per meter by the original cost price per meter and multiply by 100. Profit percentage can be calculated as: \(\frac{0.16C}{C} * 100 = 0.16 * 100 = 16\%\) So, the profit percentage is \(16\%\). The correct answer is (d) none of these.

Key concepts

Markup Calculation

Understanding markup calculation is essential when determining the final selling price of goods. A markup is the percentage added to the cost price of a product, to arrive at its selling price. This addition ensures that the seller makes a profit. To calculate the markup, first identify the cost price of the product. In our example, the adjusted cost of cloth is recalculated due to under-measurement. The cost price becomes only 80% of the original cost due to a 20% deduction, leading to an effective cost of \(0.8C\). Next, the shopkeeper applies a 20% markup on this adjusted cost. A markup of 20% means you multiply the adjusted cost by 1.2 (since 100% + 20% = 120% or 1.2 in decimal form). Therefore, the selling price (\(S\)) becomes \(0.8C \times 1.2\). This markup calculation helps in setting a selling price that ensures a margin over the cost price.

Cost Calculation

Cost calculation is the fundamental step to understanding profitability. It involves determining how much was initially paid for the goods. In this scenario, the cost is affected by the shopkeeper's error or strategy in measuring less cloth than standard.Originally, the cost for a full meter of cloth would be \(C\). However, with the shopkeeper under-measuring by 20%, the effective cost drops to \(0.8C\). This reduced cost is significant as it forms the base for further profit calculations and contrasts with the final selling price to determine overall gain.It's crucial to accurately calculate this cost to establish a baseline against which all further calculations are made. Only by understanding the true cost can one apply markup and find the eventual profit and profit percentage. This grasp of cost impacts pricing strategies and decisions around markup and profit margins.

Percentage Increase

The concept of percentage increase is used to understand how much more one value is compared to another. It highlights how a certain percentage addition affects the original value. In our exercise, the percentage increase applies when the shopkeeper adds a markup on the newly calculated cost price. The markup is a 20% increase on the effective cost of the cloth. It’s calculated by multiplying the effective cost by a factor of 1.2 (which is 100% of the original cost plus the 20% increase). This kind of percentage calculation is extraordinarily handy for businesses when determining price setting for goods and adapting pricing strategies. It allows a business to plan their profit margin accurately by anticipating and executing these percentage calculations.

Sales Price Calculation

Calculating the sales price is the final step in leveraging all previously calculated values to determine what amount a customer will pay. Sales price considers any cost adjustments and markups.Based on our scenario, the sales price is calculated after determining the adjusted cost due to the shopkeeper's measurement and the applied markup. With the adjusted cost at \(0.8C\) and a markup of 20%, the formula for the sales price becomes \(S = 0.8C \times 1.2\), providing the amount consumers will actually pay.Having calculated the sales price aids shopkeepers in knowing the expected revenue per unit sold and influences financial planning and projections. It is a crucial component of overall sales strategy and pricing policy.