Question

Find two consecutive numbers such that the difference of their reciprocals is 1/4 the reciprocal of the small number.

Answer 1

let the two numbers be x and x+1

then 1/x - 1/(x+1) = 1/4(1/x)

multiply by 4x(x+1)

4(x+1) - 4x = x + 1


x = 3

So the two numbers are 3 and 4

Check: 1/3 - 1/4 = 1/12
1/4 of 1/3 = 1/12