Q.An agent received ₹4,200 as commission on sales of ₹1,05,000. Find the rate of commission.

The rate is the commission expressed as a percentage of the turnover.

$=4\%$.

Let the rate of commission be $r\%$. Since $\text{commission}=\dfrac{r}{100}\times\text{turnover}$, we reverse it:

Simplify: $\dfrac{4200}{105000}=\dfrac{42}{1050}=\dfrac{1}{25}=0.04$, so $r=0.04\times100=4$.

Independent check: $4\%$ of ₹1,05,000 is $\tfrac{4}{100}\times105000=₹4{,}200$, exactly the commission given.

Dividing turnover by commission instead of commission by turnover, or forgetting to multiply by 100 (which leaves the answer as 0.04 rather than 4%).