The present worth of a bill due 7 months hence is ₹1200. If the bill were due at the end of $$2\frac{1}{2}$$ years, its present worth would be ₹1016. What is the rate per cent of the bill?

Let us first understand what the questions ask. We are given that the bill has a certain present value, which seems to be reducing over time. 

We are given that the bill is 1200 rupees after 7 months and 1016 rupees after 2.5 years. That means the calculation for future value considering the current value of the bill using a rate of bill over the years is being done. 

We can write the equation that, Present value equals=$$1200\left(1+\frac{7}{12}\left(\frac{x}{100}\right)\right)$$

We can also write the equation that, Present value equals=$$1016\left(1+2.5\left(\frac{x}{100}\right)\right)$$

Let us equate both these equations by taking x/100 as z

$$1200\left(1+\frac{7}{12}z\right)=1016\left(1+2.5z\right)$$

$$1200+700z=1016+2540z$$

$$184=1840z$$

$$z=0.1$$

$$\frac{x}{100}=0.1$$

$$x=10\%$$