The sum of two numbers is 1215 and their HCF is 81. If the numbers lie between 500 and 700, then the sum of the reciprocals of the numbers is .........

HCF of the two numbers is 81 so two numbers are 81x and 81y.

81(x + y) = 1215

x + y = 15

numbers lie between 500 and 700 so,

For the first number - 

81 $$\times$$ 7 = 567

For the second number- 

$$81 \times 8$$ = 648

sum of both numbers = 567 + 648 = 1215

The sum of the reciprocals of the numbers = $$\frac{1}{81x} + \frac{1}{81y}$$

= $$\frac{81x + 81y}{81x \times 81y} = \frac{1215}{567 \times 648} = \frac{1215}{367416}$$

= $$\frac{5}{1512}$$