The price of wheat ,per kg , is increased by `17.5%` and the quantity of wheat bought is decreased by `10%` .What is the percentage change in the amount spent on wheat ?

Options

A. Increase , `5.44%`
B. Decrease , `5.75%`
C. Decrease , `5.44%`
D. Increase , `5.75%`

Answer

To solve the problem step by step, we will calculate the percentage change in the amount spent on wheat after the price increase and quantity decrease.

### Step 1: Define the variables
Let the original price of wheat per kg be \( A \) and the original quantity of wheat bought be \( M \).

### Step 2: Calculate the new price of wheat
The price of wheat is increased by \( 17.5\% \). Therefore, the new price \( P \) can be calculated as:
\[ P = A + (17.5\% \text{ of } A) = A + 0.175A = 1.175A \]

### Step 3: Calculate the new quantity of wheat
The quantity of wheat bought is decreased by \( 10\% \). Therefore, the new quantity \( Q \) can be calculated as:
\[ Q = M - (10\% \text{ of } M) = M - 0.1M = 0.9M \]

### Step 4: Calculate the original amount spent on wheat
The original amount spent \( S_{\text{original}} \) can be calculated as:
\[ S_{\text{original}} = \text{Original Price} \times \text{Original Quantity} = A \times M = AM \]

### Step 5: Calculate the new amount spent on wheat
The new amount spent \( S_{\text{new}} \) can be calculated as:
\[ S_{\text{new}} = \text{New Price} \times \text{New Quantity} = (1.175A) \times (0.9M) = 1.0575AM \]

### Step 6: Calculate the change in amount spent
The change in the amount spent can be calculated as:
\[ \text{Change} = S_{\text{new}} - S_{\text{original}} = 1.0575AM - AM = (1.0575 - 1)AM = 0.0575AM \]

### Step 7: Calculate the percentage change in amount spent
The percentage change can be calculated as:
\[ \text{Percentage Change} = \left( \frac{\text{Change}}{S_{\text{original}}} \right) \times 100 = \left( \frac{0.0575AM}{AM} \right) \times 100 = 5.75\% \]

### Final Answer
The percentage change in the amount spent on wheat is \( 5.75\% \).

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