Question

If the sum of two number is 55 and the h.c.f and l.c.f are 5 and 120 respectively the sum of reciprocal of the numbers is equal to?

Answer 1

Let the numbers be a and b.

 
Then, a + b = 55 and ab = 5 x 120 = 600.

 
The required sum

=1/a+1/b 

= a+b/ab

= 55/600

=11/120

Answer 2

Let the numbers be n1 and n2

Then n1×n2=5×120(product of two numbers =product of their hcf and lcm)

n1+n2=55(given)

Now 1/n1+1/n2=(n1+n2)/(n1×n2)
=55/(5×120)
=11/120

HOPE THIS HELPS!!!