The price of tomato increases by 10%. The consumption of tomato decreases by 15%. What is the percentage change in the expenditure on tomatoes?

Let's assume the initial price of tomato and it's consumption is 10y and 10z respectively.

So total expenditure on tomatoes initially = 10y $$\times$$ 10z = 100yz

The price of tomato increases by 10%.

price of tomato after increase = 10y of (100+10)%

= 10y of 110%

= $$10y\times\frac{110}{100}$$

= 11y

The consumption of tomato decreases by 15%.

consumption of tomato now = 10z of (100-15)%

= 10z of 85%

= $$10z\times\frac{85}{100}$$

= 8.5z

total expenditure on tomatoes after the change in the price and consumption = 11y$$\times$$8.5z

= 93.5yz

Percentage change in the expenditure on tomatoes = $$\frac{\left(100yz-93.5yz\right)\times\ 100}{100yz}$$

= $$\frac{6.5yz\times\ 100}{100yz}$$

= 6.5% decrease