A and B started a business with the investments of Rs. (z-2000) and Rs. (z+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?

Solution

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 = [(z-2000)+(z+4000)]/2 - 1000 = [2z+2000]/2 - 1000 = z+1000-1000 = z The ratio between the investment of A, B and C with respect to the time = (z-2000)x12 : (z+4000)x4 : zx8 = (z-2000)x3 : (z+4000) : zx2 The ratio between the profits of B and C is 5:8 respectively. (z+4000)/2z = 5/8 (z+4000)/z = 5/4 4z+16000 = 5z 5z-4z = 16000 z = 16000 Required percentage = [(z-2000)/z]x100 = [(16000-2000)/16000]x100 = [14000/16000]x100 = 14000/160 = 87.5%