Question

If the sum of two numbers is 55 and the h.c.f. and l.c.m of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:op 1:

Answer 1

Let the numbers be a and b.

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

sum of reciprocal= $\frac{1}{a} + \frac{1}{b} = \frac{b+a}{ab} = \frac{55}{600} = \frac{11}{120}$