The simple interest on a certain sum for $$8\frac{4}{7}$$​ years at the rate of 6.8% per annum is Rs. 7,344. What will be the amount payable on the same sum at the rate of 9.7% per annum simple interest in $$6\frac{2}{3}$$​years?

Correct option is C

Given:

Simple Interest (SI) for $$8\frac{4}{7} = \frac{60}{7}$$​ years

Rate = 6.8% p.a.

SI = Rs. 7344 

For second case; 

Rate = 9.7%, Time = $$\frac{20}{3}$$​ years

Formula Used:

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

Amount = Principal + New SI

Solution:

From first case:

​$$7344 = \frac{P \times 6.8 \times \frac{60}{7}}{100} \\ \ \\734400 = P \times 6.8 \times \frac{60}{7} \\ \ \\P = \frac{734400 \times 7}{6.8 \times 60} \\ \ \\P = \frac{5130800}{408} = Rs. 12,600$$​​

Now for the second case:

SI = $$\frac{12600 \times 9.7 \times \frac{20}{3}}{100}$$​​

= $$\frac{12600 \times 9.7 \times 20}{300}$$​​

= $$\frac{2432580}{300}$$​ = Rs. 8,148

Amount = 12600 + 8148 = Rs. 20,748