A reduction of 20% in the price of wheat enables a person to buy 3.5 kg more wheat for Rs.770. The original price of rice is

Options

A. Rs. 55 per kg
B. Rs.45 per kg
C. Rs. 65 per kg
D. Rs. 37 per kg

Answer

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

### Step 1: Understand the given data
We know that there is a reduction of 20% in the price of wheat, and this allows a person to buy 3.5 kg more wheat for Rs. 770.

**Hint:** Identify the key values from the problem statement: reduction percentage, increase in quantity, and total amount spent.

### Step 2: Convert the percentage reduction to a fraction
A reduction of 20% can be expressed as a fraction:
\[ 20\% = \frac{20}{100} = \frac{1}{5} \]

**Hint:** Remember that percentages can be converted into fractions by dividing by 100.

### Step 3: Determine the increase in quantity in terms of percentage
If the price is reduced by 20%, then the remaining price is 80% of the original price. The increase in quantity can be calculated using the relationship between the decrease in price and the increase in quantity.

If the price decreases by 20%, the increase in quantity can be calculated as:
\[ \text{Increase in quantity} = \frac{\text{Reduction percentage}}{100 - \text{Reduction percentage}} \times 100 \]
Here, we can see that:
\[ \frac{20}{80} = \frac{1}{4} \quad \text{(which is 25% increase)} \]

**Hint:** To find the percentage increase in quantity, use the formula relating reduction and increase.

### Step 4: Relate the percentage increase to the actual increase in kg
We know that a 25% increase corresponds to an increase of 3.5 kg. We can set up a proportion to find out how much 100% would be:
\[ 25\% \text{ corresponds to } 3.5 \text{ kg} \]
Let \( x \) be the amount of wheat that corresponds to 100%:
\[ \frac{25}{100} = \frac{3.5}{x} \]
Cross-multiplying gives:
\[ 25x = 3.5 \times 100 \]
\[ 25x = 350 \]
\[ x = \frac{350}{25} = 14 \text{ kg} \]

**Hint:** Use cross-multiplication to solve proportions effectively.

### Step 5: Calculate the price per kg of wheat
Now that we know the person can buy 14 kg of wheat for Rs. 770, we can find the price per kg:
\[ \text{Price per kg} = \frac{770}{14} \]
Calculating this gives:
\[ \text{Price per kg} = 55 \text{ Rs.} \]

**Hint:** To find the unit price, divide the total cost by the total quantity.

### Conclusion
The original price of wheat is Rs. 55 per kg.

**Final Answer:** Rs. 55 per kg