divide 41000 into two parts such that their amounts at 50% compound interest compounded annually in 2 and 3 years are equal

24600 , 16400

Step-by-step explanation:

Let the first part be x

So, second part will be 41000 - x

For amount x

SI = prt / 100

SI = x * 0.50 * 2

SI = 1x

For amount 41000 - x

SI = (41000-x) * 0.50 * 3

SI = 61500 - 1.5x

1x = 61500 - 1.5x

1.5x + x = 61500

2.5x = 61500

x = 61500 / 2.50 = 24600 for 2 years

2nd part = 41000 - 24600 = 16400 for three years

i believe the correct answers are:

4x+3y=31: parallel

-3x+4y=8: perpendicular

3x+4y=12: neither

-4x+3y=-1: neither