​The simple interest on a certain sum for $$4\frac{2}{5}$$​years at the rate of 9.5% p.a. is Rs. 3,553. What will be the amount payable on the same sum at 8.4% p.a. simple interest in $$7\frac{1}{2}$$years?

Correct option is B

​Given:

SI for 4$$\frac{2}{5}$$​ years at 9.5% = Rs. 3,553

Find amount at 8.4% for 7$$\frac{1}{2}$$​ years.

Formula Used:

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

where, P is principal, R is rate, T is time

Solution:

Principal using SI formula:

$$3,553 = \frac{P \times 9.5 \times \frac{22}{5}}{100} \\ \ \\ \Rightarrow \quad P = 8,500$$​​

Now, SI at 8.4% for 7$$\frac{1}{2}$$​ years:

​$$\text{SI} = \frac{8,500 \times 8.4 \times \frac{15}{2}}{100} = 5,355$$

Thus, 

Total amount: $$A=8,500+5,355= ₹13,855$$​​