Answer:
[tex]The \ two \ numbers \ are \ \frac{1}{6} \ and \ \frac{5}{6}[/tex]
Step-by-step explanation:
Let the two numbers be = x , y
Given:
One of the number is 5 times other number, that is y = 5x ----- ( 1 )
The sum of their reciprocals is 36/5 , that is
[tex]\frac{1}{x} + \frac{1}{y} = \frac{36}{5}[/tex] ------ ( 2 )
Substitute y in the second equation.
[tex]\frac{1}{x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{1 \times 5}{5 \times x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{5}{5x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{5+1}{5x} = \frac{36}{5}\\\\\frac{6}{5x} =\frac{36}{5}\\\\36 \times 5x = 6 \times 5\\\\x = \frac{6 \times 5}{36 \times 5} = \frac{1}{6}[/tex]
Substitute x in first equation.
[tex]y = 5x\\\\y = 5 \times \frac{1}{6} \\\\y = \frac{5}{6}[/tex]
