Question

Wheat is now being sold at Rs. 27 per kg. During last month, its cost was Rs. 24 per kg. Find by how much per cent a family should reduce its consumption so as to keep the expenditure fixed.

• A. 10.2%
• B. 12.1%
• C. 12.3%
• D. 11.1%

Hint:

Use a fixed budget and compare how much wheat it buys at the old and new price.

Answer 1

The Correct Option is D

Step 1: Find the percentage rise in price.
Increase in price \(= 27 - 24 = 3\) rupees per kg. Percentage increase \(= \frac{3}{24} \times 100 = 12.5\%\).

Step 2: Recall the formula linking price rise to consumption cut.
To keep expenditure the same when price rises by \(a\%\), consumption must fall by \(\frac{a}{100+a} \times 100\%\). This works because expenditure = price \(\times\) quantity, and it must stay constant.

Step 3: Substitute \(a = 12.5\).
Reduction \(= \frac{12.5}{100+12.5} \times 100 = \frac{12.5}{112.5} \times 100\).

Step 4: Simplify and check the wrong options.
\(\frac{12.5}{112.5} \times 100 = 11.11\%\), which rounds to 11.1%. Option B, 12.1%, and option C, 12.3%, both wrongly use the 12.5% price rise itself instead of applying the correct reduction formula, so they are wrong.

Final Answer:
The family must cut consumption by \[ \boxed{11.1\%} \]