A vendor sells apples at 10 for Rs. 1 gaining 40%. How many apples did he buy for Rs. 1?

Answer

To solve the problem step by step, we will determine how many apples the vendor bought for Rs. 1, given that he sells 10 apples for Rs. 1 and gains 40%.

### Step 1: Understand the Selling Price
The vendor sells 10 apples for Rs. 1. Therefore, the selling price (SP) of 10 apples is:
\[ SP = 1 \text{ Rs.} \]

### Step 2: Calculate the Gain Percentage
The gain percentage is given as 40%. This means that the cost price (CP) of the apples is less than the selling price. The formula to find the cost price based on the selling price and gain percentage is:
\[ CP = \frac{100}{100 + \text{Gain Percentage}} \times SP \]

### Step 3: Substitute the Values
Substituting the values into the formula:
\[ CP = \frac{100}{100 + 40} \times 1 \]
\[ CP = \frac{100}{140} \times 1 \]
\[ CP = \frac{100}{140} = \frac{5}{7} \text{ Rs.} \]

### Step 4: Find the Cost Price of 1 Apple
Since the cost price we calculated is for 10 apples, we need to find the cost price for 1 apple:
\[ CP \text{ of 1 apple} = \frac{5}{7} \div 10 = \frac{5}{70} = \frac{1}{14} \text{ Rs.} \]

### Step 5: Calculate the Number of Apples Bought for Rs. 1
To find out how many apples the vendor bought for Rs. 1, we can use the cost price of one apple:
\[ \text{Number of apples} = \frac{1 \text{ Rs.}}{CP \text{ of 1 apple}} = \frac{1}{\frac{1}{14}} = 14 \]

### Final Answer
The vendor bought **14 apples** for Rs. 1.

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