Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulum is

As two pendulums begin two swings simultaneously, then
$n_1{T}_1=n_2{T}_2$
Where, $n_1$ and $n_2$ are the number of oscillations of first and second pendulum respectively and $T_1$ and $T_2$ be their respective time periods.
The time period of simple pendulum is given by
$T=2\pi \sqrt{\frac{l}{g}}$
where, l =length of pendulum
and g = acceleration due to gravity
$\Rightarrow T^2\propto 1$ …. (ii)
So, from Eqs. (i) And (ii), we get
$\frac{l_1}{l_2}=\frac{T_1^2}{T_2^2}=\frac{n_2^2}{n_1^2}$
Here, $n_1=9,n_2=7$
$\Rightarrow \frac{l_1}{l_2}=\frac{{\left(7\right)}^2}{{\left(9\right)}^2}\frac{49}{81}$
Hence, the ratio of pendulum lengths
$l_1:l_2=49:81$