The price of food items increases by 50%. By what percentage should a family reduce their consumption, such that their food expenditure decreases by 40%?

Let the initial consumption be 100 kg and the initial cost of food be Rs. 100 per kg.

Initial Food expenditure = 100 x 100 = Rs. 10,000

The price of food items increases by 50%.

New price of food items = 1.5 x 100 = Rs. 150 per kg

The food expenditure has to decrease by 40%

New targeted food expenditure = 60% of 10000 = Rs. 6,000

New consumption = 6000/150 = 40 kg

Reduction in consumption = 100 – 40 = 60 kg

% reduction in consumption = (60/100) x 100 = 60%

Hence, option a.