Let the amounts invested at 10% and 8% be Rs.x and Rs.y respectively.
Then as per the question
x × 10 × 1/ 100 = y × 8 × 1/ 100 = 1350
10x + 8y = 135000 …………..(i)
After the amounts interchanged but the rate being the same, we have
x × 8 × 1/ 100 = y × 10 × 1/ 100 = 1350 – 45
8x + 10y = 130500 …………….(ii)
Adding (i) and (ii) and dividing by 9, we get
2x + 2y = 29500 ……………(iii)
Subtracting (ii) from (i), we get
2x – 2y = 4500
Now, adding (iii) and (iv), we have
4x = 34000
x = 34000/4 = 8500
Putting x = 8500 in (iii), we get
2 × 8500 + 2y = 29500
2y = 29500 – 17000 = 12500
y = 12500/2 = 6250
Hence, the amounts invested are Rs. 8,500 at 10% and Rs. 6,250 at 8%.