A and B started a business with the investments of Rs. (y-2000) and Rs. (y+4000) respectively. After 4 months of the start of the business, B left it and C joined it. The initial investment of C is Rs. 1000 less than the average of the initial investment of A and B together. If at the end of one year, the ratio between the profits of B and C is 5:8 respectively, then find out the initial investment of A is what percentage of the initial investment of C?

The initial investment of C is Rs. 1000 less than the average of the initial investment of A and B together.

initial investment of C = [(y-2000)+(y+4000)]/2 - 1000

= [2y+2000]/2 - 1000

= y+1000-1000

= y

The ratio between the investment of A, B and C with respect to the time = (y-2000)x12 : (y+4000)x4 : yx8

= (y-2000)x3 : (y+4000) : yx2

The ratio between the profits of B and C is 5:8 respectively.

(y+4000)/2y = 5/8

(y+4000)/y = 5/4

4y+16000 = 5y

5y-4y = 16000

y = 16000

Required percentage = [(y-2000)/y]x100

= [(16000-2000)/16000]x100

= [14000/16000]x100

= 14000/160

= 87.5%