Latest Tech Mahindra Aptitude Question SOLUTION: The arithmatic mean of 2 no is 34 and geomatric mean of two no is 16 then nos will be

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The arithmatic mean of 2 no is 34 and geomatric mean of two no is 16 then nos will be

Asked In Tech Mahindra (10 years ago)

Solved Avishek Pattanaik Read Solution (11)

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Read Solution (11) :

Avishek Pattanaik  (10 years ago)

Let the 2 nos. be 'a' and 'b'
Arithmetic mean=(a+b)/2=34 i.e. a+b=68 -----------eqn.1
Geometric mean=(ab)^(1/2)=16 i.e. ab=256
a-b=[(a+b)^2}-4ab]^(1/2)
or, a-b= [(68^2)-(4*256)]^(1/2)=60-------------------eqn.2
Solving eqn.1 &2 we get--
a=64 & b=4
Answer: two nos are 64 & 4

Is this solution Helpfull? Yes (42) | No (1)  

Manasa Nikitha  (10 years ago)

A.M of a and b=>(a+b)/2=34=> a+b=68---(1)
G.M of a and b=>sqrt(a,b)=16=> ab=256
(a-b)^2=(a+b)^2-4ab= (68)^2-(4*256)=>4624-1024=> 3600
(a-b)^2=3600=> a-b=60------(2)
Solving (1) and (2), we get
b=4, a=64

Is this solution Helpfull? Yes (9) | No   

saurav  (10 years ago)

use the options, it will be quicker :P

Is this solution Helpfull? Yes (7) | No   

Ayush Rastogi  (10 years ago)

let nos are a,b
so A.M = (a+b)/2= 34
-----> a+b=68
G.M. sqrrot of ab=16
-----> ab=16*16
soving them a=64, b=4

Is this solution Helpfull? Yes (4) | No (1)  

PARVY GOVIL  (10 years ago)

a+b /2 =34
(ab)^1/2 =16
taking different case of a and b we gt a=4 b=64

Is this solution Helpfull? Yes (1) | No   

sachin kumar  (10 years ago)

i think it can be 2 solutions
a=4 and b=64
a=64 and b=4

if i take 1 case
a+b/2 that is 4+64/2=34
sqrt(4*64)=16

if i take 2 case
a+b/2 ie 64+4/2=34
sqrt(64*4)=16

Is this solution Helpfull? Yes (1) | No (1)  

Amitava  (10 years ago)

From experience the equation will be
a^2-(34x2)a+16^2=0
a^-68a+256=0
Solving..
a = 4 or 64
That's the two numbers.

Is this solution Helpfull? Yes | No   

abhishek pal  (10 years ago)

(X+Y)/2 = 34
SQRT(XY)= 16
(X-Y)^2= (X+Y)^2 - 4XY
ANS = 4 AND 64

Is this solution Helpfull? Yes | No   

Shravya sure  (10 years ago)

arithmatic mean (a+b)/2=34
geometric mean sqrt(ab)=16
so
a+b=68
ab=16*16 that is 16*4*4 = 64*4( its sum is 68)
so the numbers are 64 and 4

Is this solution Helpfull? Yes | No   

arpana singh  (10 years ago)

x+y/2=34;xy^1/2=16
x,y=4,64 or 64,4

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mani  (10 years ago)

a+b=68 -->equ 1
ab=256 -->equ 2
b=256/a
sub b in 1
a+256/a=68
a^2 + 256=68a
a^2-68a+256=0
a=4 or 64
ans : a= 4, b=64 or a=64 ,b=4

Is this solution Helpfull? Yes | No   

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