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 

Let LCM $=28x$

HCF $=x$

The sum of their LCM and HCF is  $28x+x=29x$

According to the problem

The sum of their LCM and HCF is 1740

$29x=1740\Rightarrow x=60$

HCF $=60$

LCM $=28\times 60$

One of the numbers is 240

The product of two numbers $=$ Their LCM $\times$HCF

$240\times b=28\times 60\times 60$

$b=\frac{28\times 60\times 60}{240}$

Another number $b=420$