Decomposition of A is a first order reaction at T(K) and is given...

For the reaction $A(g) \rightarrow B(g) + C(g)$, initially pressure of A is 1 bar.
Initially: total pressure = 1 bar.
After 100 min: total pressure = 1.5 bar.
Using initial and final pressures, if x bar of A decomposes, then A becomes (1-x), B = x, C = x.
Total pressure = 1-x+x+x = 1+x = 1.5, so x = 0.5 bar.
For a first-order reaction: $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]}$.
Using pressures instead: $k = \frac{2.303}{100} \log \frac{1}{0.5}$
$=\frac{2.303}{100} \times \log 2 = \frac{2.303 \times 0.3}{100} = \frac{0.691}{100}$
$= 6.91 \times 10^{-3}$ min$^{-1}$ ≈ $6.9 \times 10^{-3}$ min$^{-1}$