Q: To maintain the same expenditure on rice when the price increases from Rs. 6 per kg to Rs. 8 per kg, how much must a person reduce their consumption of sugar?  

To maintain the same expenditure on rice when the price increases from Rs. 6 per kg to Rs. 8 per kg, a person must reduce their consumption of sugar by 25%.

To see this, suppose that a person was originally spending X rupees on rice, and consuming Y kg of sugar. Then, the original cost of the sugar can be expressed as 6X rupees/Y kg.

When the price of rice increases to Rs. 8 per kg, the person must reduce their consumption of sugar in order to maintain the same expenditure on rice. Let's say they reduce their consumption of sugar to Y - Z kg, where Z is the amount of sugar they need to reduce.

The cost of the sugar after the reduction is (8X rupees)/(Y - Z kg). Setting this equal to the original cost of the sugar, we have:

(8X rupees)/(Y - Z kg) = 6X rupees/Y kg

Solving for Z, we find that Z = (3/4)Y. In other words, the person must reduce their consumption of sugar by 25% in order to maintain the same expenditure on rice when the price increases from Rs. 6 per kg to Rs. 8 per kg