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Question

The sum of two numbers is 18 and the sum of their reciprocals is 14, Find the numbers.

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Solution

Let the two numbers be x and y.
According to the question, x+y=18(i)
1x+1y=14( ii )
Eq. (ii) can be re - written as y+xxy=14( iii )
On putting the value of x+y=18 in Eq. (iii), we get 18xy=14
xy=72
x=72y
On putting the value of x=72y in Eq. (i), we get,
72y+y=18
72+y2=18y
y218y+72=0
y212y6y+72=o
y(y12)6(y12)=0
(y6)(y12)=0
y=6 and 12
If y=6, then x=726=12
If y=12, then x=7212=6
Hence, the two numbers are 6 and 12.

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