At what rate of compound interest per annum, sum of Rs 20000 becomes…

Amount = P$(1 + \frac{R}{100})^t$

Here, Amount = Rs 23152.50

P = Rs 20000

Time = 1 year 6 months = 3 compounds because it is compounded half yearly

Thus, 

23152.50 = 20000$(1 + \frac{R}{100})^3$

$\frac{23152.50}{20000}  =  (1 + \frac{R}{100})^3$

$\sqrt[3]{\frac{23152.50}{20000} } =  \frac{100 + R}{100}$

Solving, R = 5%

Rate of compound interest per annum = 10% per annum