Answer : Option B

Explanation :

Let the rate of interest be R% per annum.
Assume that Rs. 10000 amount to Rs. 160000 in T years
$MF#%10000\left(1 + \dfrac{\text{R}}{100}\right)^\text{T} = 160000\\\\ => \left(1 + \dfrac{\text{R}}{100}\right)^\text{T} = \dfrac{160000}{10000} = 16\\\\ => \left(1 + \dfrac{\text{R}}{100}\right)^\text{T/2} = \sqrt{16}= 4 \quad \color{#F00}{\text{--- (1)}}$MF#%
$MF#%\text{In T/2 years, Rs.10000 amounts to }10000\left(1 + \dfrac{\text{R}}{100}\right)^\text{T/2} \\\\ = 10000 \times 4 \quad \color{#F00}{ \text{[∵ from (1)]}}\\\\ = 40000$MF#%