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, we will follow these steps:

### Step 1: Define the initial price and quantity
Let the initial price of wheat per kg be \( P \) and the initial quantity bought be \( Q \).

### Step 2: Calculate the new price after the increase
The price of wheat is increased by 17.5%. Therefore, the new price \( P' \) can be calculated as:
\[ P' = P + (17.5\% \text{ of } P) = P + \frac{17.5}{100} \times P = P \times \left(1 + \frac{17.5}{100}\right) = P \times 1.175 \]

### Step 3: Calculate the new quantity after the decrease
The quantity of wheat bought is decreased by 10%. Therefore, the new quantity \( Q' \) can be calculated as:
\[ Q' = Q - (10\% \text{ of } Q) = Q - \frac{10}{100} \times Q = Q \times \left(1 - \frac{10}{100}\right) = Q \times 0.9 \]

### Step 4: Calculate the initial amount spent
The initial amount spent on wheat can be calculated as:
\[ \text{Initial Amount} = P \times Q \]

### Step 5: Calculate the new amount spent
The new amount spent on wheat can be calculated as:
\[ \text{New Amount} = P' \times Q' = (P \times 1.175) \times (Q \times 0.9) = P \times Q \times 1.175 \times 0.9 \]

### Step 6: Simplify the new amount spent
Now, we can simplify the new amount spent:
\[ \text{New Amount} = P \times Q \times 1.0575 \]

### Step 7: Calculate the percentage change in the amount spent
The percentage change in the amount spent can be calculated using the formula:
\[ \text{Percentage Change} = \frac{\text{New Amount} - \text{Initial Amount}}{\text{Initial Amount}} \times 100 \]
Substituting the values we have:
\[ \text{Percentage Change} = \frac{(P \times Q \times 1.0575) - (P \times Q)}{P \times Q} \times 100 \]
This simplifies to:
\[ \text{Percentage Change} = \frac{P \times Q \times (1.0575 - 1)}{P \times Q} \times 100 = (1.0575 - 1) \times 100 = 0.0575 \times 100 = 5.75\% \]

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

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