If a sum amounts to ₹12,900 at the end of the 4th year and ₹14,250 at the end of the 5th year at simple interest, what is the rate of interest?

In simple interest, the increase in amount per year is constant.

Amount at end of 5th year = ₹14,250
Amount at end of 4th year = ₹12,900

Interest for 1 year = ₹14,250 − ₹12,900 = ₹1,350

So, yearly interest = ₹1,350

Interest for 4 years = $4 \times 1350 = 5400$

Principal:
$P = 12900 - 5400 = 7500$

Now, rate:
$r = \frac{100 \times 1350}{7500} = 18%$

So, the rate of interest is 18% per annum.