Question

A man buys an item for Rs. 1200 and sells it at a gain of 15%. The selling price of the item is:

• A. Rs. 1370
• B. Rs. 1270
• C. Rs. 1350
• D. Rs. 1380

Hint:

To easily calculate percentages mentally, break down the percentage: \(15\%\) of \(1200\) can be viewed as \(10\% + 5\%\). \(10\%\) of \(1200 = 120\). \(5\%\) is half of that, which equals \(60\). Adding them together: \(120 + 60 = 180\). Finally, \(1200 + 180 = 1380\).

Answer 1

The Correct Option is D

Concept: In commercial arithmetic, transactions involve Cost Price (C.P.), Selling Price (S.P.), and Profit/Gain percentage. A gain means the item was sold for more than its purchase price.
• Selling Price Formula for Gain: \[ \text{S.P.} = \text{C.P.} \times \left(1 + \frac{\text{Gain \%}}{100}\right) \]
• Alternatively, \(\text{S.P.} = \text{C.P.} + \text{Profit Value}\), where \(\text{Profit Value} = \frac{\text{Gain \%}}{100} \times \text{C.P.}\)

Step 1: Identifying values given in the problem statement.
The parameters presented are: Cost Price (C.P.) &= Rs. 1200
Gain Percentage &= 15%

Step 2: Calculating the actual absolute monetary gain value.
The financial profit made is \(15\%\) of the original purchase cost price: \[ \text{Profit} = \frac{15}{100} \times 1200 \] Simplifying the expression by cancelling out the double zeros in the numerator and denominator: \[ \text{Profit} = 15 \times 12 \] Let us carry out this multiplication systematically: \[ 15 \times 12 = 15 \times (10 + 2) = (15 \times 10) + (15 \times 2) = 150 + 30 = 180 \] So, the total profit earned on the item is Rs. 180.

Step 3: Finding the final Selling Price.
We add the computed profit value directly to our core base cost price: \[ \text{S.P.} = \text{C.P.} + \text{Profit} \] \[ \text{S.P.} = 1200 + 180 = 1380 \] Thus, the retail selling price of the item must be set at Rs. 1380. This matches Option (D).