The LCM of two numbers is \(28\) times of their HCF. The sum of their LCM and HCF is \(1740\). If one of the numbers is \(240\), then the other number is: দুটি সংখ্যার LCM তাদের HCF এর \(28\) গুণ। LCM এবং HCF এর যোগফল \(1740\)। যদি একটি সংখ্যা \(240\) হয়, তবে অন্য সংখ্যাটি কত?

Let HCF \(= h\). Then LCM \(= 28h\).

Given:

\[ 28h + h = 1740 \]

\[ 29h = 1740 \]

\[ h = 60 \]

So, LCM \(= 28 \times 60 = 1680\).

We know:

\[ \text{First Number} \times \text{Second Number} = \text{LCM} \times \text{HCF} \]

\[ 240 \times \text{Second Number} = 1680 \times 60 \]

\[ \text{Second Number} = \frac{1680 \times 60}{240} \]

\[ \text{Second Number} = 420 \]

Correct Answer: D