Question

Due to a reduction of $6\frac{1}{4}\%$ in the price of rice, Sanjeev is able to buy $1\text{ kg}$ more for Rs 120. Then :
A. the original rate of rice = Rs 8 per kg
B. the reduced rate of rice = Rs 7.20 per kg
C. 40% of the original rate of rice = Rs 3.20
D. 80% of the reduced rate of rice = Rs 6 per kg
Choose the correct answer from the options given below:

• A. A and B Only
• B. A and C Only
• C. A, C and D Only
• D. B, C and D Only

Hint:

Using fractional equivalents of percentages saves time:
A price reduction of $\frac{1}{16}$ means the price ratio is $16 : 15$.
Since expenditure is constant, the quantity ratio is the inverse: $15 : 16$.
The difference in quantity is $16 - 15 = 1$ ratio unit.
Since 1 ratio unit corresponds to 1 kg:
Original quantity = 15 kg.
Original price = $\frac{120}{15} = \text{Rs } 8$ per kg.
This ratio method avoids any algebraic equations.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This problem is based on the inverse relationship between the price of a commodity and its consumption when the total expenditure is constant.
The price of rice decreases, which allows a buyer to purchase more of it for the same total sum of Rs 120.
We need to calculate the original and reduced prices per kilogram and verify the truth value of the given statements.

Step 2: Key Formula or Approach: 1. Let the original price of rice be $x$ per kg.
2. The percentage reduction in price is: \[ 6\frac{1}{4}\% = 6.25\% = \frac{25}{400} = \frac{1}{16} \] 3. The reduced price is: \[ x \left(1 - \frac{1}{16}\right) = \frac{15}{16}x \] 4. The quantity bought originally with Rs 120 is $\frac{120}{x}$.
5. The quantity bought at the reduced price is $\frac{120}{\frac{15}{16}x} = \frac{128}{x}$.
6. The difference in quantity is 1 kg: \[ \frac{128}{x} - \frac{120}{x} = 1 \]

Step 3: Detailed Explanation:

• Calculate the Original Rate ($x$): Solve the quantity equation: \[ \frac{128 - 120}{x} = 1 \] \[ \frac{8}{x} = 1 \implies x = 8 \] So, the original rate of rice is Rs 8 per kg. (This means Statement A is True).

• Calculate the Reduced Rate: \[ \text{Reduced Rate} = \frac{15}{16} \times 8 = \text{Rs } 7.50 \text{ per kg} \] (This means Statement B is False, as it states the reduced rate is Rs 7.20).

• Verify Statement C: We need to find 40% of the original rate: \[ 40\% \text{ of } 8 = \frac{40}{100} \times 8 = 0.4 \times 8 = \text{Rs } 3.20 \] Since this matches Statement C, Statement C is True.

• Verify Statement D: We need to find 80% of the reduced rate: \[ 80\% \text{ of } 7.50 = \frac{80}{100} \times 7.50 = 0.8 \times 7.5 = \text{Rs } 6.00 \] Since this matches Statement D, Statement D is True.

Step 4: Final Answer:
Statements A, C, and D are true, while Statement B is false.
Therefore, the correct option is (C).