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The arithemetic mean and the geometric m...

The arithemetic mean and the geometric mean of two distinct 2-digit numbers x and y are two integers one of which can be obtained by reserving the digits of the other (in base 10 representation). Then x + y equals

A

82

B

116

C

130

D

148

Text Solution

Verified by Experts

The correct Answer is:
C
`(x+y)/(2)=10 a+b, sqrt(xy)=10 b+a" "(a, b in N)`
`xy=(10b+a)^(2)`
`(x-y)^(2)=4(11a+11b)(9a-9b)`
`=4.11 . (a+b). 9(a-b)`
`rArr a+b=11, a-b=1`
`a=6, b=5`
`((x-y)^(2)" is perfect square of an integer")`
`x+y=130`
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