A shopkeeper has certain number of apples of which 10% are found to tbe rotten. He sels 85% of the remaining good apples and still has 405 good apples. How may apples did he originally have?

Options

A. A)`3500`
B. B)`3000`
C. C)`2500`
D. D)`2000`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the total number of apples
Let the total number of apples the shopkeeper originally had be \( K \).

### Step 2: Calculate the number of rotten apples
Since 10% of the apples are rotten, the number of rotten apples is:
\[ \text{Rotten apples} = 0.10 \times K = \frac{K}{10} \]

### Step 3: Calculate the number of good apples
The number of good apples remaining after removing the rotten ones is:
\[ \text{Good apples} = K - \text{Rotten apples} = K - \frac{K}{10} = \frac{10K}{10} - \frac{K}{10} = \frac{9K}{10} \]

### Step 4: Calculate the number of good apples sold
The shopkeeper sells 85% of the remaining good apples, which means he retains 15% of the good apples:
\[ \text{Good apples remaining} = 0.15 \times \text{Good apples} = 0.15 \times \frac{9K}{10} \]

### Step 5: Set up the equation based on the information given
According to the problem, after selling 85% of the good apples, the shopkeeper has 405 good apples left. Therefore, we can set up the equation:
\[ 0.15 \times \frac{9K}{10} = 405 \]

### Step 6: Solve for \( K \)
Now, let's simplify the equation:
\[ \frac{1.35K}{10} = 405 \]
Multiplying both sides by 10:
\[ 1.35K = 4050 \]
Now, divide both sides by 1.35:
\[ K = \frac{4050}{1.35} \]
Calculating this gives:
\[ K = 3000 \]

### Conclusion
The shopkeeper originally had **3000 apples**.

---