Question

If the sum of two no.is 20.if the sum of their reciprocal is 5/24.find the no?

Answer 1

let the two numbers be x and 20-x

given

$\frac{1}{x} + \frac{1}{20 - x} = \frac{5}{24} \\ \\ \frac{20 - x + x}{x(20 - x)} = \frac{5}{24} \\ {x}^{2} - 20x + 96 = 0 \\ \\ {x}^{2} - 12x - 8x + 96 = 0 \\ \\ x(x - 12) - 8(x - 12) = 0 \\ \\ (x - 12)(x - 8) = 0 \\ \\ x = 8 \\ \\ x = 12$

Therefore the numbers are 8 and 12.

hope it helps.