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 _____.
Answer & explanation
Correct answer: option 3
Let the numbers be 81x and 81y, then
81x + 81y = 1215
x + y = 15
Possible pair of x + y are = (1, 14), (2, 13) and (4, 11) an (7, 8)
Number should be between 500 and 700, then
x = 7 and y = 8
First number = 81 × 7 = 567
Second number = 81 × 8 = 648
Sum of the reciprocals of the numbers is = \(\frac{1}{567}\) + \(\frac{1}{648}\) = \(\frac{1}{81}\)(\(\frac{1}{7}\) + \(\frac{1}{8}\)) = $\frac{5}{1512}$