A gas mixture of $3$ litres of propane and butane on complete combustion at ${25}^{o}C$ produced $10$ litres of $C{O}_2$. The gas mixture contains initally :

The correct option is A $2$ litres $C_3{H}_8+$ $1$ litre $C_4{H}_{10}$
The balanced reactions are given below:
$C_3{H}_8+5O_2\to 3C{O}_2+4H_{2}O$
$a$
$C_4{H}_{10}+\frac{13}{2}{O}_2\to 4C{O}_2+5H_{2}O$
$b$
$\therefore a+b=3$ ...(i)
Volume of $C{O}_2$ formed $=3a+4b$
$\therefore 3a+4b=10$ ...(ii)
By eqs. (i) and (ii) $,b=1$ and $a=2$

Hence, the gas mixture contains initially $2$ L of $C_3{H}_8$ and $1$ L of $C_4{H}_{10}$.