Question

A man sold \(\frac 35^{th}\) of his articles at a gain of 20% and the remaining at cost price. Find the percentage gain earned in the transaction.

• A. 8
• B. 10
• C. 12
• D. 14

Answer 1

The Correct Option is C

To find the percentage gain in the transaction, let's denote the total number of articles as \(x\). The man sold \(\frac{3}{5}\) of his articles at a gain of 20% and the remaining \(\frac{2}{5}\) at the cost price. Let's break it down:

• The number of articles sold at a gain = \(\frac{3}{5}x\)
• The number of articles sold at cost price = \(\frac{2}{5}x\)

Let's assume the cost price of each article is \(c\).

The selling price of articles sold at a gain:

\[ \text{Selling Price} = \left(\frac{3}{5}x\right) \times (1 + 0.20) \cdot c = \left(\frac{3}{5}x\right) \times 1.20c \]

The selling price of articles sold at cost price:

\[ \text{Selling Price} = \left(\frac{2}{5}x\right) \cdot c \]

Total selling price:

\[ SP_{\text{total}} = \frac{3}{5}x \cdot 1.20c + \frac{2}{5}x \cdot c \]

\[ SP_{\text{total}} = \left(\frac{3}{5}x \cdot 1.20 + \frac{2}{5}x\right)c \]

\[ SP_{\text{total}} = \left(\frac{3\times1.20}{5} + \frac{2}{5}\right)xc\]

\[ SP_{\text{total}} = \left(\frac{3.60}{5} + \frac{2}{5}\right)xc\]

\[ SP_{\text{total}} = \left(\frac{5.60}{5}\right)xc\]

\[ SP_{\text{total}} = 1.12xc \]

Thus, the total cost price for all articles:

\[ CP_{\text{total}} = x \cdot c \]

The percentage gain is calculated as follows:

\[ \text{Gain} = SP_{\text{total}} - CP_{\text{total}} = 1.12xc - xc = 0.12xc \]

\[ \text{Percentage Gain} = \left(\frac{\text{Gain}}{CP_{\text{total}}}\right) \times 100\% \]

\[ \text{Percentage Gain} = \left(\frac{0.12xc}{xc}\right) \times 100\% \]

\[ \text{Percentage Gain} = 0.12 \times 100\% = 12\% \]

The man earned a percentage gain of 12% in the transaction.