A sum of Rs. 46,800 is divided among A, B, C and D in such a way that the ratio of the combined share of A and D to the combined share of B and C is 8 : 5. The ratio of the share of B to that of C is 5 : 4. A receives Rs. 18,400. If x is the difference between the share of A and B and y is the difference between the share of C and D, then what is the value of (x - y) (in Rs.)?

Solution(By Examveda Team)

$$\eqalign{ & A + B + C + D = 46800 \cr & \frac{{A + D}}{{B + C}} = \frac{8}{5} \cr & \frac{B}{C} = \frac{{5P}}{{4P}},\,\,B + C = 9P \cr & \frac{{A + D}}{{9P}} = \frac{8}{5} \cr & A + D = \frac{{72}}{5}P \cr & \frac{{72}}{5}P + 9P = 46800 \cr & 117P = 46800 \times 5 \cr & P = 2000 \cr & B = 5P = 5 \times 2000 = 10000 \cr & C = 4P = 4 \times 2000 = 8000 \cr & A = 18400 \cr & D = 46800 - 10000 - 8000 - 18400 = 10400 \cr & A - B = x = 18400 - 10000 = 8400 \cr & D - C = y = 10400 - 8000 = 2400 \cr & x - y = 8400 - 2400 = 6000 \cr} $$