The price of tea increses by 20%, but family decides to increase its expenditure by only 15 %. By what percentage should they reduce their consumption

Let the original price of tea be $P$ and the original consumption be $C$.
The original expenditure is $E = P \times C$.

The price increases by 20%.
New Price ($P'$) = $P \times (1 + 0.20) = 1.20P$.

The family decides to increase its expenditure by only 15%.
New Expenditure ($E'$) = $E \times (1 + 0.15) = 1.15E$.

Let the new consumption be $C'$. We know that $E' = P' \times C'$.
Substitute the expressions for $E'$ and $P'$:
$1.15E = 1.20P \times C'$

We know $E = P \times C$. Substitute this into the equation from Step 4:
$1.15(P \times C) = 1.20P \times C'$
Divide both sides by $P$ (assuming $P \neq 0$):
$1.15C = 1.20C'$
$C' = \frac{1.15}{1.20}C$
$C' = \frac{115}{120}C = \frac{23}{24}C$

Percentage reduction = $\frac{\text{Original Consumption} - \text{New Consumption}}{\text{Original Consumption}} \times 100\%$
Percentage reduction = $\frac{C - C'}{C} \times 100\%$
Percentage reduction = $\frac{C - \frac{23}{24}C}{C} \times 100\%$
Percentage reduction = $\frac{C(1 - \frac{23}{24})}{C} \times 100\%$
Percentage reduction = $(1 - \frac{23}{24}) \times 100\%$
Percentage reduction = $(\frac{24 - 23}{24}) \times 100\%$
Percentage reduction = $\frac{1}{24} \times 100\%$
Percentage reduction = $\frac{100}{24}\%$
Percentage reduction = $\frac{25}{6}\%$
Percentage reduction = $4.166...\%$

Rounding to two decimal places, the percentage reduction is:
$\boxed{4.17\%}$