A sum of money becomes ₹14,160 in 3 years at simple interest. If the rate of interest increases by 25%, the same sum of money becomes ₹14,700 in the same time. What is the rate of interest?

Correct option is A

Given:

- Final amount after 3 years at original rate = ₹14,160

- Final amount after 3 years at increased rate = ₹14,700

- Time = 3 years

- Increase in rate = 25%
Formula Used:

- Simple Interest (SI) = $$\frac{(Principal × Rate × Time) }{ 100}$$​​

- Amount = Principal + Interest
Solution:

Let the original rate be R% and the principal be P.

From original amount:

​$$=> P + \frac{(P × R × 3)}{100 }= 14,160 \\\ \\=> P(1 + \frac{3R}{100}) = 14,160 ... (1) \\\ \\=> New rate = R + 25$$​​

Now subtract (1) from (2):

​$$=> P(1 +\frac{ 3.75R }{ 100}) - P(1 +\frac{ 3R }{ 100}) = 14,700 - 14,160 \\\ \\=> P[(1 +\frac{ 3.75R}{100}) - (1 + \frac{3R}{100})] = 540\\\ \\=> P[\frac{(3.75R - 3R)}{100}] = 540 \\\ \\=> P(\frac{0.75R }{100}) = 540 \\\ \\=> P × R = 72,000 ... (3)$$​​

Now from equation (1):

​$$=> P(1 + \frac{3R}{100}) = 14,160 \\\ \\=> P + \frac{3PR}{100 }= 14,160\\\ \\=> P + \frac{(72,000 × 3)}{100 }= 14,160 \\\ \\=> P + 2,160 = 14,160\\\ \\=> P = 12,000$$​​

Now use P = 12,000 in equation (3):

=> 12,000 × R = 72,000

=> R = 6

The original rate of interest is 6% per annum.