A clerk spends 1/5 of his salary on rent, 1/3 on transport and 1/8 on entertainment. If the remaining amount is GHS 820, find his total annual salary.

The clerk spends $\frac{1}{5}$ on rent, $\frac{1}{3}$ on transport, and $\frac{1}{8}$ on entertainment.
To add these fractions, find a common denominator, which is the least common multiple (LCM) of 5, 3, and 8. The LCM is $5 \times 3 \times 8 = 120$.

$$\text{Total fraction spent} = \frac{1}{5} + \frac{1}{3} + \frac{1}{8}$$ $$= \frac{1 \times 24}{5 \times 24} + \frac{1 \times 40}{3 \times 40} + \frac{1 \times 15}{8 \times 15}$$ $$= \frac{24}{120} + \frac{40}{120} + \frac{15}{120}$$ $$= \frac{24 + 40 + 15}{120}$$ $$= \frac{79}{120}$$

If $\frac{79}{120}$ of the salary is spent, the remaining fraction is 1 minus the total fraction spent.

$$\text{Fraction remaining} = 1 - \frac{79}{120}$$ $$= \frac{120}{120} - \frac{79}{120}$$ $$= \frac{120 - 79}{120}$$ $$= \frac{41}{120}$$

The remaining amount is GHS 820, which corresponds to $\frac{41}{120}$ of the total annual salary. Let $S$ be the total annual salary.

$$\frac{41}{120} \times S = \text{GHS } 820$$

To find $S$, multiply GHS 820 by the reciprocal of $\frac{41}{120}$.

$$S = 820 \times \frac{120}{41}$$ $$S = (820 \div 41) \times 120$$ $$S = 20 \times 120$$ $$S = \text{GHS } 2400$$

The clerk earns GHS 2400 per annum.

$$\text{GHS } 2400$$