Correct option is (B) 194400
Let both numbers are a and b.
Also let LCM and HCF of both numbers a and b are L and H respectively.
According to given conditions,
L+H = 1260 __________(1)
L = 900+H __________(2)
\(\therefore\) 900+2H = 1260 (From (1) & (2))
\(\Rightarrow\) 2H = 1260 - 900 = 360
\(\Rightarrow\) \(H=\frac{360}2=180\)
\(\therefore\) L = 900+180 = 1080
Now, product of both numbers = Product of their HCF and LCM.
i.e., a \(\times\) b = HCF (a, b) \(\times\) LCM (a, b)
\(\therefore\) Product of both numbers \(=H\times L=180\times1080\)
= 194400
