Question

If the selling price of 40 articles is same as the cost price of 50 articles, then the loss or gain percent is

• A. (20
• B. (20
• C. (25
• D. (25

Hint:

An incredibly fast mental shortcut rule for these styles of question templates is: \[ \text{Gain or Loss Percentage} = \left( \frac{\text{Number of CP articles} - \text{Number of SP articles}}{\text{Number of SP articles}} \right) \times 100 \] Substituting the values gives: (50 - 4040 100

Answer 1

The Correct Option is D

Concept: Profit and loss problems involving variable counts of articles are solved most effectively by modeling the Cost Price (CP) of a single article as a constant variable or a specific nominal value. The relations governing profit and loss are:

• (Profit (Gain) = Selling Price (SP) - Cost Price (CP))

• (Gain Percentage = ( GainTotal Cost Price ) 100

Step 1: Setup the given algebraic equation. Let the Cost Price of 1 article be denoted as (x). Therefore, the total Cost Price of 50 articles is: \[ \text{Total CP of 50 articles} = 50x \] According to the question statement, the Selling Price (SP) of 40 articles is exactly equal to the Cost Price of 50 articles. Thus, we have: \[ \text{Total SP of 40 articles} = \text{Total CP of 50 articles} = 50x \]

Step 2: Find the Selling Price of a single article to make an accurate baseline comparison. Since the total Selling Price of 40 individual articles combined is (50x), the Selling Price of exactly 1 article is: \[ \text{SP of 1 article} = \frac{50x}{40} = \frac{5}{4}x = 1.25x \]

Step 3: Determine whether a gain or loss occurred, and compute its total financial value. Comparing the cost price and selling price for 1 single article:

• (CP of 1 article = x)

• (SP of 1 article = 1.25x)
Since the Selling Price ((1.25x)) is strictly greater than the Cost Price ((x)), the transaction results in a Net Gain. \[ \text{Gain on 1 article} = \text{SP} - \text{CP} = 1.25x - x = 0.25x \]

Step 4: Compute the absolute Gain Percentage. Using the percentage formula calculated against the base Cost Price: \[ \text{Gain Percent} = \left( \frac{\text{Gain on 1 article}}{\text{CP of 1 article}} \right) \times 100 \] \[ \text{Gain Percent} = \left( \frac{0.25x}{x} \right) \times 100 \] Therefore, there is a total gain of 25