The difference between the CI and SI on a certain sum of money for 3 years at 4% percent per annum is ₹152. Find the sum invested.

Correct option is C

Given:

Rate of interest = 4%

Time = 3 years

Difference between CI and SI = ₹152

Formula Used:

Amount = $$Principle \times \left(1+ \frac{r}{100}\right)^{t}$$​​

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

Solution:

CI=$$\text{ Principle} \times \left(1+ \frac{r}{100}\right)^{t} - P$$​​

Difference = CI -SI for 3 years

​$$152= \left[Principle \times \left(1+ \frac{4}{100}\right)^{3} -P\right] - \frac{P\times 4\times 3}{100}$$​​

​$$152=P \left(1+ \frac{1}{25}\right)^{3}-1 - \frac{12}{100}$$​​

​$$152=P \left( \frac{17576}{15625}\right)-1 - \frac{3}{25}$$​​

​$$152= P \left( \frac{ 17576-15625-1875}{15625}\right)$$​​

​$$152 = P \left(\frac{76}{15625}\right)$$​​

​$$P = 152\times \frac{15625}{76}$$​​

​$$P = ₹31,250$$ 

Thus, the principle is ₹31,250