What is the greater of the two numbers whose product is 1092 and the sum of the two numbers exceeds their difference by 42 ?

Solution (By Examveda Team)

Let the numbers be x and y
Then,
$$xy = 1092.....(i)$$
And,
$$\eqalign{ & \Leftrightarrow \left( {x + y} \right) - \left( {x - y} \right) = 42 \cr & \Leftrightarrow 2y = 42 \cr & \Leftrightarrow y = 21 \cr} $$
Putting y = 21 in (i), we get :
$$x = \frac{{1092}}{{21}} = 52$$
Hence, greater number = 52