Given,
time period of the pendulum while the lift is moving upwards and downward are in the ratio,
$$
T_1: T_2=1: 2
$$

Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$
We know that,
If the lift is moving upward, then total time-period,


when the lift is moving downwards, then the total time period,

By dividing Eq. (i) to (ii), we get
$$
\begin{array}{rlrl}
\therefore & \frac{T_1}{T_2} & =\sqrt{\frac{g-a}{g+a}} \\
& \text { Now, } & \frac{1}{2} & =\sqrt{\frac{g-a}{g+a}}
\end{array}
$$
Square on the both sides, we get
$$
\begin{aligned}
& \text { or } & \left(\frac{1}{2}\right)^2 & =\frac{g-a}{g+a} \text { or } \frac{g-a}{g+a}=\frac{1}{4} \\
& \text { or } & 4 g-4 a & =g+a \text { or } 3 g=5 a \\
& \text { or } & a & =\frac{3 g}{5} \\
\Rightarrow & & a & =\frac{30}{5}=6 \mathrm{~m} / \mathrm{s}^2
\end{aligned}
$$

So, the acceleration of the lift is $6 \mathrm{~m} / \mathrm{s}^2$.