A sum of Rs. 1250 has to distributed among A, B, C and D. Total share of B and D is equal to (14/11) of total share of A and C. Share of D is half of share of A. Share of C is 1.2 of share of A. What are the shares of A, B, C and D respectively?

Solution(By Examveda Team)

$$\eqalign{ & {\text{A}} + {\text{B}} + {\text{C}} + {\text{D}} = 1250.......\left( 1 \right) \cr & \frac{{{\text{B}} + {\text{D}}}}{{{\text{A}} + {\text{C}}}} = \frac{{14}}{{11}}.......\left( 2 \right) \cr & \frac{{\text{D}}}{{\text{A}}} = \frac{1}{2} \cr & \frac{{\text{C}}}{{\text{A}}} = \frac{{1.2}}{1} = \frac{6}{5} \cr & {\text{From equation }}\left( 1 \right) \cr & 14 + 11 = 1250 \cr & 25{\text{ units}} = {\text{1250}} \cr & {\text{1 unit}} = 50 \cr & {\text{C's share 6 units}} \to {\text{300}} \cr & {\text{A's share 5 units}} \to {\text{250}} \cr} $$
\[ \Rightarrow \frac{{\text{D}}}{{\text{A}}} = \frac{1}{2}\begin{array}{*{20}{c}} { \to 125} \\ { \to 250} \end{array}\]
$$\eqalign{ & {\text{From equation }}\left( 1 \right) \cr & {\text{A}} + {\text{B}} + {\text{C}} + {\text{D}} = 1250 \cr & 250 + {\text{B}} + 300 + 125 = 1250 \cr & {\text{B}} = 575 \cr} $$