GATE Electronics and Communications (EC) 2018 Solved Paper

Let x(t) be a periodic function with period T = 10. The Fourier series coefficients for this series are denoted by a_k, that is:
$\mathit{x}\left(\mathit{t}\right)=\sum _{\mathit{k}=-\mathit{\infty }}^{\mathit{\infty }}{\mathit{a}}_{\mathit{k}}{\mathit{e}}^{\mathit{j}\mathit{k}\frac{2\mathit{\pi }}{\mathit{T}}\mathit{t}}$
The same function x(t) can also be considered as a periodic function with period T′ = 40. Let ${\mathit{b}}_{\mathit{k}}$ be the Fourier series coefficients when the period is taken as T’. If $\sum _{\mathit{k}=-\mathit{\infty }}^{\mathit{\infty }}|{\mathit{a}}_{\mathit{k}}\frac{}{}|=16$, then $\sum _{\mathit{k}=-\mathit{\infty }}^{\mathit{\infty }}|{\mathit{b}}_{\mathit{k}}\frac{}{}|$is equal to