Question

if the sum of two number is 27 and the sum of reciprocals is 30/20. find the number

Answer 1

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Let 'x' and 'y' be the two numbers

H.C.F of x & y = 3

L.C.M of x & y = 60

and, x + y = 27

Product of two numbers = H.C.F * L.C.M

⇒ xy = 3×60 = 180

then,

(1/x) + (1/y) = (x + y)/(xy) = 27/180 = 3/20 (∵ x + y = 27)

∴ the sum of reciprocal of x & y is (3/20)