The price of ghee rises by 32%. A family reduces its consumption so that its total spending on ghee increases by only 10% compared to before. If the family earlier consumed 10 kg, what is the new consumption?

Introduction / Context:
This problem ties together percentage change in price, adjustment in quantity, and overall expenditure. Expenditure = price * quantity, so multiple percentage changes combine multiplicatively, not additively.

Given Data / Assumptions:

• Original consumption = 10 kg.
• Price increases by 32% ⇒ price factor = 1.32.
• Final expenditure rises by 10% ⇒ expenditure factor = 1.10.

Concept / Approach:
If E = P * Q, then new E / old E = (new P / old P) * (new Q / old Q). Hence 1.10 = 1.32 * (Q_new / Q_old). Solve for Q_new using Q_old = 10 kg.

Step-by-Step Solution:

Verification / Alternative check:
Original spend = 10 * P. New spend = 8 1/3 * 1.32P = (25/3)*1.32P ≈ 11P, which is 10% higher than 10P.

Why Other Options Are Wrong:
8 3/4 kg and 8 1/2 kg correspond to different expenditure targets; 9 kg would give too large a spending increase; 8 1/4 kg undershoots the required 10% rise.

Common Pitfalls:
Adding or subtracting percentages linearly (32 − 10), or assuming consumption falls by exactly 32% − 10% = 22%. Always use the multiplicative relation of E = P * Q.

Final Answer:
8 1/3 kg