Answer :
Let the number be x .
Reciprocal of x :-
[tex] = \frac{1}{x} [/tex]
An equation to find x :-
[tex]2 \times \frac{1}{x} = 16 \times \frac{1}{20} [/tex]
[tex] \frac{2}{x} = \frac{16}{20} [/tex]
[tex]16 \times x = 20 \times 2[/tex]
[tex]16x = 40[/tex]
[tex]x = \frac{16}{40} [/tex]
[tex]x = \frac{4}{10} [/tex]
[tex]x= \frac{4 \div 2}{10 \div 2} [/tex]
[tex]x = \frac{2}{5} [/tex]
Reciprocal of x :-
[tex] = \frac{5}{2} [/tex]
Which means the number :-
[tex] = \frac{5}{2} [/tex]
We can check it by :-
[tex]2 \times \frac{2}{5} = \frac{16}{20} [/tex]
[tex] \frac{4}{5} = \frac{16}{20} [/tex]
[tex] \frac{4}{5} = \frac{16 \div 4}{20 \div 4} [/tex]
[tex] \frac{4}{5} = \frac{4}{5} [/tex]
LHS = RHS
Which means we have found the correct number .
Therefore , the value of the number , whose reciprocal multiplied by 2 gives 16 times the reciprocal of 20 is :-