A man invests a certain principal amount of money at 6.5% per annum simple interest and another principal amount of money at 7.5% per annum simple interest. Without reinvestment his income from interest after 3 years is Rs. 400. One fourth of first principal amount is equal to one fifth of the second principal amount. Find the approximate total sum that was invested.

Let $$'y'$$ be the principal amount invested at a 6.5% per annum rate.

Let $$'x'$$ be the principal amount invested at a 7.5% per annum rate.

It is given that, $$\frac{y}{4}=\frac{x}{5}$$............(1)

It is also given that without reinvestment, his income from interest after 3 years is Rs. 400

i.e., $$y\times\ 3\times\ 0.065+x\times\ 3\times\ 0.075=400$$

$$\frac{4x}{5}\times\ 3\times\ 0.065+x\times\ 3\times\ 0.075=400$$

$$0.381x=400$$

Hence, $$x=Rs.\ 1049.87$$, then $$y=\frac{4x}{5}=\frac{1049.87\times\ 4}{5}=Rs.\ 839.90$$

Total invested sum = $$y+x=$$ = $$1889.77\approx Rs.1890$$

Option (A) is correct.