Fifty-one tuning forks are arranged in order of increasing frequencies so that each fork gives 3 beats per second with the next. The first fork has a frequency two thirds of the last one. The frequency of the first fork is :-

When two frequencies are such that they are in the ratio 3 : 2, the first is said to be the ‘fifth’ of the second.
Let n be the frequency of the 1st ,
then frequency of the second = n+3
then frequency of the third = n + 2 x 3
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then frequency of the fifty third = n + 50 x 3
It is given that, $\frac{\mathrm{n}+50\times 3}{\mathrm{n}}=\frac{3}{2}$
$\begin{array}{l}\text{ or }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}2\mathrm{n}+300=3\mathrm{n}\\ \text{ or }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{n}=300\end{array}$