Question

The price of rice increases by 30%. A family reduced its consumption so that the expenditure of the rice is up only by 10%. If the total consumption of the rice before the price rise was 10 kg per month, then the consumption of rice per month at present (in kg) is:

• A. \(7\frac{6}{15}\)
• B. \(8\frac{1}{15}\)
• C. \(8\frac{6}{13}\)
• D. \(8\frac{5}{13}\)

Answer 1

The Correct Option is C

To solve this problem, we need to find the new consumption of rice after the price increase and expenditure adjustment. The problem states:

1. Initial price increase is 30%, so the new price becomes \(1.3\) times the old price.
2. The expenditure on rice increases by 10%, so the new expenditure is \(1.1\) times the old expenditure.
3. Before the price rise, the consumption was \(10\) kg. Let the new consumption be \(x\) kg.

We can set up the equation based on the expenditure relationship:

\(1.3 \times P \times x = 1.1 \times P \times 10\)

Where \(P\) is the original price per kg of rice. Simplifying the equation:

\[1.3x = 1.1 \times 10\]

\[x = \frac{11}{13} \times 10\]

\[x = \frac{110}{13}\]

Converting \(\frac{110}{13}\) into a mixed number:

\[\frac{110}{13} = 8 \frac{6}{13}\]

Thus, the new consumption of rice per month is \(8\frac{6}{13}\) kg.

Hence, the correct answer is \(8\frac{6}{13}\).