94 is divided into two parts in such a way that fifth part of the first and the eighth part of the second are in the ratio 3 : 4. The first part is = ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{A}} + {\text{B}} = 94 \cr & \therefore \frac{{\text{A}}}{5}:\frac{{\text{B}}}{8} = 3:4 \cr & \Rightarrow \frac{{{\text{A}} \times 8}}{{5 \times {\text{B}}}} = \frac{3}{4} \cr & \Rightarrow \frac{{\text{A}}}{{\text{B}}} = \frac{3}{4} \times \frac{5}{8} \cr & \Rightarrow \frac{{\text{A}}}{{\text{B}}} = \frac{{15}}{{32}} \cr & {\text{ A}}:{\text{B}} \cr & {\text{ }}15:32 \cr & {\text{Let }}15x:32x \cr & \therefore 15x + 32x = 47x \cr & \Rightarrow 47x = 94 \cr & \Rightarrow x = 2 \cr & \therefore {\text{A}} = 2 \times 15 = 30 \cr & {\text{B}} = 32 \times 2 = 64 \cr} $$