Question:
A vendor bought 6 toffees for a rupee. How many for a rupee must he sell to gain 20%?
A vendor bought 6 toffees for a rupee. How many for a rupee must he sell to gain 20%?
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When the investment amount is constant (e.g., one rupee), the quantity sold is inversely proportional to the price multiplier. To gain \(20%\) (which is a multiplier of \(1.2\) or \(6/5\)), you must sell \(5/6\) of the original quantity. \(6 \times (5/6) = 5\).
Updated On: May 9, 2026
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
The question gives the cost price in terms of quantity per rupee and asks for the selling price in terms of quantity per rupee to achieve a specific profit percentage.
Step 2: Key Formula or Approach:
\(\text{Selling Price (SP)} = \text{Cost Price (CP)} \times \left(1 + \frac{\text{Profit %}}{100}\right)\).
Work with the price of a single unit to avoid confusion.
Step 3: Detailed Explanation:
The vendor bought \(6\) toffees for Rs. \(1\).
Therefore, the Cost Price (CP) of \(1\) toffee is Rs. \(\frac{1}{6}\).
To gain a profit of \(20%\), the Selling Price (SP) of \(1\) toffee must be: \[ \text{SP} = \text{CP} \times \left( \frac{100 + 20}{100} \right) \] \[ \text{SP} = \frac{1}{6} \times \frac{120}{100} \] \[ \text{SP} = \frac{1}{6} \times \frac{6}{5} = \frac{1}{5} \text{ Rs.} \] This means that \(1\) toffee is sold for Rs. \(\frac{1}{5}\).
To find how many toffees are sold for Rs. \(1\), we take the reciprocal: \[ \text{Number of toffees for Rs. 1} = \frac{1}{\text{SP of 1 toffee}} = \frac{1}{1/5} = 5 \]
Step 4: Final Answer:
He must sell \(5\) toffees for a rupee.
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