Question

Tinkawala purchased the articles for Rs. 123684. He sold \(60 \%\) of those at a profit of \(16.66 \%\) and rest at a loss. Find the loss percentage on the remaining if the overall loss is \(14 \%\) ? (a) \(20 \%\) (b) \(30 \%\) (c) \(60 \%\) (d) \(66.66 \%\)

Short answer

Answer: The loss percentage on the remaining unsold articles is approximately 60%.

Step-by-step solution

Identify given information and variables

We'll first identify the given information and variables: - Total purchasing amount: Rs. 123684 - \(60 \%\) of the articles sold at a profit of \(16.66 \%\) - Overall loss: \(14 \%\) - Loss percentage on the remaining articles: ?

Calculate the sold and unsold amounts

Calculate the sold and unsold amounts by using the given percentage of sold articles: - Sold articles = \(60 \%\) of total purchasing amount = \(0.6 \times 123684\) = Rs. 74210.4 - Unsold articles: total purchasing amount - sold articles = Rs. 123684 - Rs. 74210.4 = Rs. 49473.6

Calculate the overall actual selling price

Calculate the overall actual selling price using the overall loss percent: Overall Loss (\(14 \%\)) = Total Purchasing Amount - Actual Selling Price Actual Selling Price = Total Purchasing Amount - (Overall Loss \(\times\) Total Purchasing Amount) Actual Selling Price = Rs. 123684 - (\(0.14 \times 123684\)) = Rs. 106348.64

Calculate the actual selling price of the sold articles

To find the actual selling price of the sold articles: Actual selling price = Cost price + (Profit percent * Cost price) Actual selling price of sold articles = Rs. 74210.4 + (\(0.1666 \times 74210.4\)) = Rs. 86537

Calculate the actual selling price of unsold articles

Calculate the actual selling price of the unsold articles by subtracting the actual selling price of the sold articles from the overall actual selling price: Actual selling price of unsold articles = Overall actual selling price - Actual selling price of sold articles Actual selling price of unsold articles = Rs. 106348.64 - Rs. 86537 = Rs. 19811.64

Calculate the loss percentage on the unsold articles

Finally, calculate the loss percentage on unsold articles using the following formula: Loss percent = \(\frac{\text{Cost price of unsold articles - Actual selling price of unsold articles}}{\text{Cost price of unsold articles}} \times 100\) Loss percent = \(\frac{\text{Rs. 49473.6 - Rs. 19811.64}}{\text{Rs. 49473.6}} \times 100\) Loss percent \(\approx 60 \%\) So, the loss percentage on the remaining unsold articles is approximately \(60 \%\). Therefore, the correct answer is (c) \(60 \%\).

Key concepts

Percentage Calculation

Percentage calculation is a fundamental mathematical concept that helps in comparing quantities relative to their entire amounts. It is essential for understanding profit and loss in financial transactions. Percentages are calculated by taking a part of the quantity and dividing it by the total quantity, then multiplying the result by 100 to convert it into a percent.For example, if we know that 60% of the articles were sold, it tells us that the sold articles represent 60 percent of the total articles. In mathematical terms, this is represented as:

• Percentage sold = \( \frac{\text{Part quantity}}{\text{Total quantity}} \times 100 \)
• Here, part quantity = sold articles cost = Rs. 74210.4

Understanding percentage calculations is crucial for accurately determining profits and losses, as it allows for the conversion of these differences into easy-to-grasp proportional figures.

Selling Price

The selling price is the amount at which an item is sold to a purchaser. It reflects either a profit or a loss depending on its comparison to the cost price, which is the original price paid to acquire the item.In our problem, Tinkawala sold 60% of his articles for a profit. This means the selling price was increased by the profit percentage compared to the cost price. The formula to calculate the selling price with a profit is:

• Selling Price = Cost Price + (Profit Percentage \( \times \) Cost Price)

For the unsold articles, calculating their selling price involved first determining the total selling price for all articles and comparing it with the actual selling price derived from the overall transaction. It is an essential component in determining the loss or gain resulting from the transaction.

Loss Percentage

Loss percentage is a key concept in assessing financial setbacks in trades or transactions. It quantifies how much less an item is sold for compared to its cost price. A higher loss percentage indicates a greater decrease in value.The loss percentage is computed using the formula:

• Loss Percentage = \( \frac{\text{Cost Price} - \text{Actual Selling Price}}{\text{Cost Price}} \times 100 \)

In Tinkawala's case, the unsold articles were subject to a significant loss. The remaining unsold articles' loss percentage was determined after calculating their individual selling price and comparing it to their cost price.Understanding loss percentage helps one to evaluate transactions more comprehensively and make informed decisions to minimize losses.

Quantitative Aptitude

Quantitative aptitude involves the ability to handle numerical calculations and arithmetic reasoning effectively. It is an essential skill for solving problems related to profit and loss, percentages, and selling prices. In the context of this problem, quantitative aptitude allows for:

• Quick mental calculations to determine profits and losses.
• Accurate application of percentage formulas to find selling price and loss percentages.
• Logical reasoning to analyze various components of a transaction, such as cost price, selling price, and overall profits or losses.

Possessing strong quantitative skills is crucial for students and professionals alike, as it enhances their ability to engage with practical challenges and optimize financial outcomes. By honing these skills, one becomes proficient in navigating and resolving diverse numerical tasks with confidence.