If the price of tea is increased by 40%, by how what percentage must the consumption of tea be decreased so as not to increase the expenditure?

The correct answer is $28\frac{4}{7}\%$.

Step 1: Understand the formula
When the price of a commodity increases by $r\%$, the percentage reduction in consumption required to keep the total expenditure unchanged is given by the formula:
$\text{Percentage decrease in consumption}=\left(\frac{r}{100+r}\times 100\right)\%$

Step 2: Substitute the given value
Here, the percentage increase in price, $r=40\%$.
Substituting $r=40$ into the formula:

$\text{Percentage decrease}=\left(\frac{40}{100+40}\times 100\right)\%$

$=\left(\frac{40}{140}\times 100\right)\%$

$=\left(\frac{2}{7}\times 100\right)\%$

$=\frac{200}{7}\%$

Step 3: Convert to a mixed fraction
Dividing 200 by 7 gives a quotient of 28 and a remainder of 4:
$\frac{200}{7}\%=28\frac{4}{7}\%$

Hence, the consumption of tea must be decreased by $28\frac{4}{7}\%$ so as not to increase the overall expenditure.