Latest NDA Aptitude Question SOLUTION: The harmonic mean H of two numbers is 4 and the arithmetic mean A and geometric mean G satisfy the equation 2A + G^2 = 27. The two numbers are (a) 6, 3 (b) 9, 5 (c) 12, 7 (d) 3, 1

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(#M40026505) NDA Numerical Ability question Mental Ability Keep an EYE

The harmonic mean H of two numbers is 4 and the arithmetic mean A and geometric mean G satisfy the
equation 2A + G^2 = 27. The two numbers are
(a) 6, 3 (b) 9, 5 (c) 12, 7 (d) 3, 1

Asked In NDA MAN (10 years ago)

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pratiksha sachan  (9 years ago)

HM= 2ab/a+b, GM= root ab ,AM=a+b/2
so.
2ab/a+b=4--------------- (1)
ab=2(a+b) &
a+b= ab/2
&2A=a+b
&G^2= ab
put the value in equation which is given in question.--------
a+b+ab= 27------------------(2)
ab/2+ab= 27
3ab=54
ab=18
or
a+b+2(a+b)=27 ---> a+b+2a+2b=27----> 3a+3b=27---> so. a+b= 9
so we can match the options for both value 9 &18 so ab= 18 thn 6*3=18 and a+b=9 so.. 6+3=9

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