At constant temperature on increasing the pressure of a gas by 5% will decrease its volume by

The correct option is 4.76%.

Step-by-Step Derivation:

According to Boyle's Law, for a given mass of gas at a constant temperature, the pressure of the gas is inversely proportional to its volume:
$P·V=\text{constant}$
Let the initial pressure of the gas be $P_1$ and the initial volume be $V_1$.

When the pressure of the gas is increased by 5%, the new pressure $P_2$ becomes:
$P_2=P_1+5\%\text{of}{P}_1$
$P_2=P_1+0.05P_1=1.05P_1$

Using Boyle's law, the relationship between initial and final states is:
$P_1{V}_1=P_2{V}_2$
Substituting $P_2=1.05P_1$ into the equation:
$P_1{V}_1=1.05P_1{V}_2$
Dividing both sides by $P_1$ gives:
$V_2=\frac{V_1}{1.05}$

The decrease in volume ($\Delta V$) is calculated as:
$\Delta V=V_1-V_2$
$\Delta V=V_1-\frac{V_1}{1.05}=V_1\left(1-\frac{1}{1.05}\right)=V_1\left(\frac{0.05}{1.05}\right)$

The percentage decrease in volume is given by:
$\text{Percentage decrease in volume}=\frac{\Delta V}{V_1}$
$\text{Percentage decrease in volume}=\frac{V_1\left(\frac{0.05}{1.05}\right)}{V_1}$

Therefore, the volume of the gas will decrease by 4.76%.