If Rs.1066 are divided among A, B, C and D such that A : B = 3 : 4, B : C = 5 : 6 and C : D = 7 : 5, Who will get the maximum ?

Answer:- 1

Explanation:-

Solution:

\begin{aligned} A : B = 3 : 4, \\ B : C = 5 : 6 \\ = (5 \times \frac{4}{5}) : (6 \times \frac{4}{5}) \\ = 4 : \frac{24}{5}, \\ C : D = 7 : 5 \\ = (7 \times \frac{24}{35}) : (5 \times \frac{24}{35}) \\ = \frac{24}{5} : \frac{24}{7} . \\ ∴ A : B : C : D \\ = 3 : 4 : \frac{24}{5} : \frac{24}{7} \\ = 105 : 140 : 168 : 120. \end{aligned}

$\eqalign{ & {\text{A}}:{\text{B}} = {\text{3}}:{\text{4}}, \cr & {\text{B}}:{\text{C}} = {\text{5}}:{\text{6}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {5 \times \frac{4}{5}} \right):\left( {6 \times \frac{4}{5}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 4:\frac{{24}}{5}, \cr & {\text{C}}:{\text{D}} = {\text{7}}:{\text{5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {7 \times \frac{{24}}{{35}}} \right):\left( {5 \times \frac{{24}}{{35}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{24}}{5}:\frac{{24}}{7}. \cr & \therefore {\text{A}}:{\text{B}}:{\text{C}}:{\text{D}} \cr & = 3:4:\frac{{24}}{5}:\frac{{24}}{7} \cr & = 105:140:168:120. \cr}$ Clearly, C will get the maximum.