The difference of two numbers is 4. If the difference of their reciprocals is $\frac{4}{21}$ , find the numbers.

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Solution

Let the two numbers be x and y,
given that,
x- y =4
x = y + 4 -----(i)
and
$1 over y minus 1 over x equals 4 over 21 fraction numerator x minus y over denominator x y end fraction equals 4 over 21 fraction numerator 4 over denominator x y end fraction equals 4 over 21 x y equals 21$
From (i)

So, when y = 3; x = y+ 4 = 7

Or, when y = -7; x = y+ 4 = -3

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