The simple interest on a sum for 6 years is ₹29250. The rate of interest for the first 2 years is 7 percent per annum and for the next 4 years is 16 percent per annum. What is the sum?

Correct option is A

Given:
Simple Interest for 6 years = ₹29250
Rate of interest for the first 2 years = 7% per annum
Rate of interest for the next 4 years = 16% per annum
​Formula Used:
Simple Interest = $$\frac{P \times R \times T}{100}$$​​
where P is the principal, R is the rate of interest, and T is the time in years.

Solution:​​

Simple Interest for the first 2 years:

​$$\text{SI}_1 = \frac{P \times 7 \times 2}{100} = \frac{14P}{100} = \frac{7P}{50}$$​​

Simple Interest for the next 4 years:
​$$\text{SI}_2 = \frac{P \times 16 \times 4}{100} = \frac{64P}{100} = \frac{16P}{25}$$​​

Total Simple Interest:

​$$\frac{7P}{50} + \frac{16P}{25} = 29250$$​​

​$$\frac{7P}{50} + \frac{32P}{50} = 29250 \\ \ \\\frac{39P}{50} = 29250$$​

39P = $$29250 \times 50$$​​

39P = 1462500

P = $$\frac{1462500}{39}$$​ = 37500

The sum is ₹37500.

Thus, the correct option is (a) ₹37500.

Alternate Method:

Let, Principal =100% and SI = R % $$\times$$ T

Total SI = $$2 \times 7\% + 4 \times 16\% =78\%$$
Principal = $$\frac{29250}{78\%} \times 100\%$$ =  ₹37500.​