Question

A vegetable vendor by means of his false balance defrauds to the extent of \(10%\) in buying goods and also defrauds to \(10%\) in selling, then the gain percent is

• A. \(11\frac{1}{9}%\)
• B. \(10%\)
• C. \(22\frac{2}{9}%\)
• D. \(20%\)

Hint:

Standard formula for cheating both ways (same %): $\frac{(% \text{cheat on buy} + % \text{cheat on sell}) \times 100}{100 - % \text{cheat on sell}}$.
Here: $\frac{(10 + 10) \times 100}{100 - 10} = \frac{2000}{90} = 22.22%$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Defrauding in buying means receiving more quantity than what is paid for. Defrauding in selling means providing less quantity than what is charged for.
Step 2: Key Formula or Approach:
\[ \text{Profit ratio} = \frac{\text{Quantity received while buying}}{\text{Quantity given while selling}} \] Step 3: Detailed Explanation:
1. Buying phase: Vendor pays for \(100\) g but cheats to get \(10%\) more.
Effective quantity received = \(110\) g.
Cost of these \(110\) g = Price of \(100\) g.
2. Selling phase: Vendor charges for \(100\) g but cheats to give \(10%\) less.
Effective quantity given = \(90\) g.
Revenue from these \(90\) g = Price of \(100\) g.
3. Combining: To find profit, we compare the cost of one unit vs revenue from one unit.
Effective CP per gram = \(100/110\) price units.
Effective SP per gram = \(100/90\) price units.
\[ \frac{SP}{CP} = \frac{100/90}{100/110} = \frac{110}{90} = \frac{11}{9} \] 4. Gain % = \((\frac{11}{9} - 1) \times 100 = \frac{2}{9} \times 100 = 22.22...% = 22\frac{2}{9}%\).
Step 4: Final Answer:
The total gain percent is \(22\frac{2}{9}%\).