The time in which $\text{Rs. }80,000$ amounts to $\text{Rs. }92,610$ at $10\%$ per annum compound interest, interest being compounded semi-annually, is:

Given:
Principal ($P$) = $\text{Rs. }80,000$
Amount ($A$) = $\text{Rs. }92,610$
Rate ($R$) = $10\%$ per annum $=5\%$ semi-annually

Let the number of half-years be $n$.
The formula for compound interest compounded semi-annually is:

$$A=P{\left(1+\frac{R}{100}\right)}^n$$

Substituting the values:

$$92610=80000{\left(1+\frac{5}{100}\right)}^n$$

$$\frac{92610}{80000}={\left(\frac{105}{100}\right)}^n$$

$$\frac{9261}{8000}={\left(\frac{21}{20}\right)}^n$$

$${\left(\frac{21}{20}\right)}^3={\left(\frac{21}{20}\right)}^n$$

Comparing the exponents:

$$n=3\text{ half-years}$$

Therefore, $\text{Time}=\frac{3}{2}=1.5\text{ years}$.