Due to decrease in price of wheat by `10%` , a person is able to buy 50 gram more wheat for Rs. 1. Find the amount of wheat a person was able to buy for Rs. 1 initially.

Options

A. 400
B. 450
C. 500
D. 600

Answer

To solve the problem, we need to determine how much wheat a person was able to buy for Rs. 1 initially, given that due to a decrease in price by 10%, the person can buy an additional 50 grams of wheat for the same amount.

### Step-by-Step Solution:

1. **Understand the Price Decrease**:
The price of wheat has decreased by 10%. This means if the original price of wheat is \( P \), the new price after the decrease is:
\[ \text{New Price} = P - 0.1P = 0.9P \]

2. **Set Up the Initial and New Quantities**:
Let \( x \) be the initial quantity of wheat (in grams) that can be bought for Rs. 1 at the original price \( P \). Therefore, the quantity of wheat that can be bought at the new price \( 0.9P \) for Rs. 1 is:
\[ \text{New Quantity} = \frac{1}{0.9P} \]

3. **Express the New Quantity in Terms of the Initial Quantity**:
Since the person can buy 50 grams more wheat after the price decrease, we can set up the equation:
\[ \frac{1}{0.9P} = x + 50 \]

4. **Relate the Initial Quantity to the Price**:
The initial quantity \( x \) can also be expressed in terms of the price:
\[ x = \frac{1}{P} \]

5. **Substituting the Initial Quantity into the Equation**:
Substitute \( x \) into the equation from step 3:
\[ \frac{1}{0.9P} = \frac{1}{P} + 50 \]

6. **Clear the Fractions**:
Multiply through by \( 0.9P \) to eliminate the fractions:
\[ 1 = 0.9 + 50 \cdot 0.9P \]

7. **Rearranging the Equation**:
Rearranging gives:
\[ 1 - 0.9 = 50 \cdot 0.9P \]
\[ 0.1 = 45P \]

8. **Solve for P**:
Divide both sides by 45:
\[ P = \frac{0.1}{45} = \frac{1}{450} \]

9. **Calculate the Initial Quantity**:
Now, substitute \( P \) back to find \( x \):
\[ x = \frac{1}{P} = 450 \text{ grams} \]

### Final Answer:
The amount of wheat a person was able to buy for Rs. 1 initially is **450 grams**.