The price of rice has increased by `20%`. Lalu has decided to spend only `8%` more than what he initially did on buying rice. What is the percentage decrease in Lalu’s rice 'consumption?

Options

A. `10%`
B. `13%`
C. `18%`
D. `14%`

Answer

To solve the problem step by step, we will analyze the situation of Lalu's rice consumption after the price increase and his decision to spend more on rice.

### Step 1: Determine the initial price of rice.
Let’s assume the initial price of rice is ₹100 per kg.

### Step 2: Calculate the new price of rice after the increase.
The price of rice has increased by 20%. Therefore, the new price can be calculated as follows:
\[ \text{New Price} = \text{Initial Price} + \left( \frac{20}{100} \times \text{Initial Price} \right) = 100 + 20 = ₹120 \text{ per kg} \]

### Step 3: Determine Lalu's new expenditure.
Lalu has decided to spend 8% more than what he initially spent on rice. His initial expenditure was ₹100 (since he bought 1 kg of rice). The new expenditure will be:
\[ \text{New Expenditure} = \text{Initial Expenditure} + \left( \frac{8}{100} \times \text{Initial Expenditure} \right) = 100 + 8 = ₹108 \]

### Step 4: Calculate the quantity of rice Lalu can buy with the new expenditure.
Now, we need to find out how much rice Lalu can buy with ₹108 at the new price of ₹120 per kg:
\[ \text{Quantity of Rice} = \frac{\text{New Expenditure}}{\text{New Price}} = \frac{108}{120} \text{ kg} \]
This simplifies to:
\[ \text{Quantity of Rice} = \frac{108}{120} = \frac{9}{10} \text{ kg} \]

### Step 5: Calculate the decrease in rice consumption.
Initially, Lalu was buying 1 kg of rice. Now he is buying \(\frac{9}{10}\) kg. The decrease in consumption is:
\[ \text{Decrease in Consumption} = 1 - \frac{9}{10} = \frac{1}{10} \text{ kg} \]

### Step 6: Calculate the percentage decrease in consumption.
To find the percentage decrease in consumption, we use the formula:
\[ \text{Percentage Decrease} = \left( \frac{\text{Decrease in Consumption}}{\text{Initial Consumption}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Decrease} = \left( \frac{\frac{1}{10}}{1} \right) \times 100 = 10\% \]

### Conclusion:
The percentage decrease in Lalu's rice consumption is **10%**.

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