The price of rice falls by 35%. How much extra quantity of rice can be bought with the money that was sufficient to buy 104 kg of rice previously?

Options

A. 42kg
B. 45.5kg
C. 56kg
D. 52kg

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the original price of rice.
Let's assume the original price of rice is \( P \) per kg. According to the problem, we can take \( P = 100 \) rupees per kg.

### Step 2: Calculate the price after the decrease.
The price of rice falls by 35%. Therefore, the new price can be calculated as follows:
\[ \text{New Price} = P - (35\% \text{ of } P) = P - 0.35P = 0.65P \]
Substituting \( P = 100 \):
\[ \text{New Price} = 0.65 \times 100 = 65 \text{ rupees per kg} \]

### Step 3: Calculate the total money spent on 104 kg of rice at the original price.
The total money spent to buy 104 kg of rice at the original price is:
\[ \text{Total Money} = \text{Quantity} \times \text{Original Price} = 104 \text{ kg} \times 100 \text{ rupees/kg} = 10400 \text{ rupees} \]

### Step 4: Calculate how much rice can be bought with the same amount of money at the new price.
Now, we will find out how much rice can be bought with 10400 rupees at the new price of 65 rupees per kg:
\[ \text{Quantity of Rice} = \frac{\text{Total Money}}{\text{New Price}} = \frac{10400 \text{ rupees}}{65 \text{ rupees/kg}} = 160 \text{ kg} \]

### Step 5: Calculate the extra quantity of rice.
To find the extra quantity of rice that can be bought, we subtract the original quantity from the new quantity:
\[ \text{Extra Quantity} = \text{New Quantity} - \text{Original Quantity} = 160 \text{ kg} - 104 \text{ kg} = 56 \text{ kg} \]

### Final Answer:
The extra quantity of rice that can be bought is **56 kg**.

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