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Question

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


Solution

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

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