Question

the difference of two numbers is 4 and the difference of their reciprocals is 4/21.

Answer 1

x - y = 4
1/y - 1/x = 4/21 [We reversed the order because since x>y so their reciprocals will also be reversed. 1/y > 1/x]
(x-y)/x.y =4/21
4/x.y = 4/21
x.y = 21
Solving these give x = 7
y = 3