The simple interest on a certain sum \(3\frac{1}{3}\) year at the rate 4.2% per annum is ₹5,845. What will be the amount payble on the same sum at the rate of 6.4% per annum simple interest in \(12\frac{1}{2}\) years?

Step 1: Convert time

$ 3\frac{1}{3} = \frac{10}{3} \text{ years}, \quad 12\frac{1}{2} = \frac{25}{2} \text{ years} $

Step 2: Use SI formula

$ \text{SI} = \frac{P \times R \times T}{100} $

Given:
$ 5845 = \frac{P \times 4.2 \times \frac{10}{3}}{100} $

Simplify:
$ 5845 = \frac{P \times 42}{300} = \frac{P \times 7}{50} $

So,
$ P = \frac{5845 \times 50}{7} = 41750 $

Step 3: Find new SI

$ \text{SI} = \frac{41750 \times 6.4 \times \frac{25}{2}}{100} $

Simplify:
$ = \frac{41750 \times 80}{100} = 41750 \times 0.8 = 33400 $

Step 4: Amount

$ \text{Amount} = P + SI = 41750 + 33400 = 75150 $

Final Answer: ₹75,150