When the price of wheat increases by 32% a family adjusts its consumption so that the total expenditure on wheat rises by only 10%; if they earlier consumed 30 kg per month, what is the new monthly wheat consumption of the family?

Introduction / Context:
This problem focuses on how a change in price and a controlled change in total expenditure affects the quantity of a commodity consumed. It is a classic example of price elasticity style reasoning that appears in aptitude tests. The family faces a price increase for wheat and decides not to let their monthly expenditure grow proportionally, so the only way to achieve this is by reducing the quantity consumed.

Given Data / Assumptions:

• Original monthly consumption of wheat is 30 kg.
• Original price of wheat is P per kg.
• Original expenditure is P * 30.
• Price increases by 32%, so new price is 1.32 * P.
• New expenditure is only 10% more than before, so it becomes 1.10 times the original expenditure.
• New quantity consumed is q kg per month, which we need to determine.

Concept / Approach:
The fundamental relation is Expenditure = Price * Quantity. If both price and expenditure change by different percentages, the quantity must adjust to keep the equality valid. We treat the initial expenditure as a baseline and then relate the new expenditure, price, and quantity with multiplicative factors. Dividing one side by the new price factor gives the new quantity factor, from which we compute the new quantity and finally the reduction in consumption.

Step-by-Step Solution:
Let initial price be P and original quantity be 30 kg.Original expenditure = P * 30.Price increases by 32%, so new price = 1.32 * P.Expenditure is to increase by only 10%, so new expenditure = 1.10 * (P * 30) = 33 * P.Let new quantity be q kg. Then new expenditure = 1.32 * P * q.Equate the two expressions for new expenditure: 1.32 * P * q = 33 * P.Cancel P to get 1.32 * q = 33, so q = 33 / 1.32 = 25 kg.

Verification / Alternative check:
Check with actual numbers. Suppose original price P is Rs. 10 per kg. Original consumption is 30 kg, so expenditure is Rs. 300. After price increase, new price is 10 * 1.32 = Rs. 13.2 per kg. New quantity is 25 kg as found. New expenditure = 13.2 * 25 = Rs. 330. This is exactly a 10% increase from Rs. 300 to Rs. 330. Therefore, the answer of 25 kg is consistent and verifies the calculation.

Why Other Options Are Wrong:
27 kg would give an expenditure of 27 * 13.2 = 356.4, which is far more than 10% above the original 300.

24 kg gives 24 * 13.2 = 316.8, which is only 5.6% approximately above 300, not the required 10%.

21 kg gives 21 * 13.2 = 277.2, which is actually lower than the original expenditure, contradicting the condition that expenditure increases by 10%.

Common Pitfalls:
Many learners attempt to subtract percentage changes directly, such as 32% minus 10%, and assume a 22% reduction in quantity. This does not work because the variables are multiplicatively related, not additively. Another common error is to treat the 10% as applied to the new price instead of the overall expenditure. Always define variables carefully, express both old and new expenditure explicitly, and then equate them. Consistent use of percentage multipliers like 1.10 and 1.32 helps avoid arithmetic confusion.

Final Answer:
The new monthly wheat consumption of the family is 25 kgs.