If the product of two positive numbers be 1575 and their ration is 7 : 9, then the greatest number is :

Answer: Option A

Let the numbers are 7x and 9x
According to the question,
$$\begin{array}{rl}& \Rightarrow 7x\times 9x=1575\\ & \Rightarrow 63x^2=1575\\ & \Rightarrow x^2=25\\ & \Rightarrow x=5\end{array}$$
Then greater number
= 9x
= 9 × 5
= 45