An investor places a total amount of ₹5,00,000 in three different funds yielding simple interest at 6%, 8% and 10% per annum respectively.
The annual interest from the 8% fund exceeds the interest from the 6% fund by ₹4,000, while the combined annual interest from all three funds is ₹41,000.
(i) Taking the amounts invested in the three funds as variables, write three linear equations representing the given information.
(ii) Determine the determinant of the coefficient matrix of the system obtained in part (i) and comment on the nature of the system (consistent / inconsistent / infinitely many solutions).
(iii) If the system is consistent with a unique solution, find the exact amount invested in each fund.