📅 Mixed & Date-Based

1. Borrow-and-lend. The same money earns interest on one side and costs interest on the other. Since the principal $P$ and time $T$ are identical on both sides, the net gain is simply $\dfrac{P\times(\text{rate gap})\times T}{100}$ — no need to compute the two interests separately.

2. SI set equal to a CI. First find the side you can compute fully (the compound interest), then equate. The handy fact: for 2 years at $r\%$ the effective CI rate is $2r+\dfrac{r^2}{100}\%$, so 10% gives 21% (not 20%) — that extra 1% is interest-on-interest. Then set your unknown $\text{SI}=\dfrac{P\times R\times T}{100}$ equal to that number and solve.

3. Comparing two investors. When the principal is the same, the interest is proportional to $R\times T$. So compare the $R\times T$ products directly: $\text{SI}_1:\text{SI}_2=R_1T_1:R_2T_2$.

4. Time given in days. Convert days to years with $T=\dfrac{\text{days}}{365}$ and plug into the same formula. If the dates are the 1st of each month, count whole months instead: $T=\dfrac{\text{months}}{12}$. To count days between two dates the standard rule is exclude the first day, include the last. Examiners pick the gap so it lands on a neat fraction — memorise $73\text{ days}=\dfrac15$ year, $146\text{ days}=\dfrac25$ year, and $91\text{ days}\approx\dfrac14$ year. Always cancel $\dfrac{P}{100}$ first to keep the numbers small.