Question

The cost price of an article ' \(A\) ' is Rs. 160 and selling price of another article ' \(B^{\prime}\) is Rs. 240 . If the selling price of \(A\) will be equal to the cost price of \(B\), then the profit after selling \(A\) is \(20 \%\). What is the profit on 'B'? (a) \(16.66 \%\) (b) \(50 \%\) (c) \(25 \%\) (d) none of these

Short answer

Answer: The profit percentage on article B is 25%.

Step-by-step solution

Determine the selling price of A when it's equal to the cost price of B.

We are given that the cost price of A is Rs. 160, and the profit after selling A is 20%. Therefore, to calculate the selling price of A, we use the formula: Selling Price = Cost Price + Profit As Profit = 20% of Cost Price, we can write: Selling Price = 160 + (20/100)*160 = 160 + 32 = Rs. 192 So, the selling price of A is Rs. 192, which is equal to the cost price of B.

Calculate the cost price of B.

As A's selling price is equal to B's cost price, B's cost price is Rs. 192.

Calculate the profit percentage on B.

We know the selling price of B' is Rs. 240, and its cost price is equal to the cost price of B (Rs. 192). To calculate the profit percentage on B, use the formula: Profit Percentage = ((Selling Price - Cost Price) / Cost Price) * 100 Profit Percentage = ((240 - 192) / 192) * 100 Profit Percentage = (48 / 192) * 100 = 25 % So, the profit on B is (c) 25%.

Key concepts

cost price

The cost price is essentially the amount you pay to purchase an item or manufacture it, considering all expenses incurred. It's the baseline price before any profit is added. In this exercise, we talk about two articles, A and B. The cost price of article A is Rs. 160. This means Rs. 160 is the complete expense involved in acquiring article A.

When dealing with such problems, it's useful to note that knowing the cost price is vital for any profit calculation. This value tells us how much we initially spent, and it's from here that we determine what our profit or loss will be, depending on the selling price. For article B in our example, the cost price isn't initially provided directly but is concluded through another calculation – it turns out to be Rs. 192, which is deductively found to be equal to the selling price of A.

selling price

The selling price is the amount a product is sold for and is the price at which it is offered to the customer. It usually includes the cost price plus any profit markup. Knowing how to calculate this figure helps determine whether you have made a profit or a loss when an item is sold.

In the problem, the selling price of article A is crucial. It's mentioned that article A sells for Rs. 192, which also equates to the cost price of article B. This connection is essential to solving the problem and finding the overall profit percentage for article B. For article B, the selling price is given as Rs. 240. By knowing both its selling price and cost price, one can calculate the profit earned from selling this article.

profit percentage

Profit percentage is a measure of profitability that depicts how much profit is made on an item relative to its cost price, expressed as a percentage. It's calculated using the formula:

• Profit Percentage = ((Selling Price - Cost Price) / Cost Price) * 100

In our given example, article A provides a 20% profit. This indicates that for every Rs. 100 spent initially, Rs. 20 is gained as profit, showing a profitable transaction compared to the cost price. For article B, after determining its cost price (Rs. 192) and selling price (Rs. 240), we can find the profit percentage:

Profit Percentage is \((240 - 192) / 192 \times 100 \) which results in 25%

This profit percentage tells us that selling article B resulted in a 25% gain over its cost price, making it a more profitable item relative to its costs.