Question

The sum of two numbers is 15 and the sum of their reciprocals is 3/10. Find the numbers

Answer 1

Let the numbers be x & y

Then x+y=15 ..........1)
1/x + 1/y = 3/10 .......2)

on solving 2)
(x+y)/xy = 3/10
or 3xy = 10*(x+y) = 10*15 = 150
or xy=150/3 = 50

Now (x-y)^2 = (x+y)^2 - 4xy = 15^2 - 4*50 = 225-200 = 25
therefore, x-y = 5
or x=y+5 .........(3)

putting the value of x in eq1)
x+y=15
or y+5+y = 15
or 2y = 10
or y=5

As x+y=15
or x=15-y=15-5=10

Ans. The no. are 10 & 5