Ratio of three numbers x, y, z are in 2, 3, 5 respectively and the sum of x, y, z is 80. If the number z is given by the equation z = ax - 8, then a is ?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let numbers are }} \cr & x = 2r,{\text{ }}y = 3r,{\text{ }}z = 5r \cr & {\text{Sum, }}x + y + z = 2r + 3r + 5r \cr & \Rightarrow x + y + z = 10r \cr & \Rightarrow x + y + z = 80 \cr & r = 8,x = 16,y = 24,z = 40 \cr & {\text{Then, }}z = ax - 8 \cr & \Rightarrow 40 = a \times 16 - 8 \cr & \Rightarrow a = 3 \cr} $$