Two numbers are in the ratio 11/2 : 22/3 When each of these is increased by 15, they become in the ratio 12/3 : 21/2 . The greater of the numbers is = ?

Answer: Option C

$$\begin{array}{rl}& \text{A : B}\\ & \frac{3}{2}:\frac{8}{3}\end{array}$$
take L.C.M. of denominator and multiply)
$$\Rightarrow \frac{3}{2}\times 6:\frac{8}{3}\times 6=9x:16x$$
After adding 15 in each we get
$$\begin{array}{rl}& \therefore \frac{9x+15}{16x+15}=\frac{5}{3}\times \frac{2}{5}\\ & \Rightarrow \frac{9x+15}{16x+15}=\frac{2}{3}\left(\text{cross multiply}\right)\\ & \Rightarrow 27x+45=32x+30\\ & \Rightarrow 5x=15\\ & \Rightarrow x=3\\ & \therefore \text{Smaller number}\\ & =\text{9}\times \text{3 = 27}\\ & \text{Greater number}\\ & \text{ = 16}\times \text{3 = 48}\end{array}$$