Latest MBA Aptitude Question SOLUTION: The sum of two numbers is 20 and there Geometric mean is 20% lower than their arithmetic mean .Find the ratio of the numbers?kindly post solution as well

1) 4:1
2)

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The sum of two numbers is 20 and there Geometric mean is 20% lower than their arithmetic mean .Find the ratio of the numbers?kindly post solution as well

1) 4:1
2) 9:1
3) 1:1
4) 17:3

Asked In MBA (11 years ago)

Solved MohanRaj Read Solution (8)

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Read Solution (8) :

Vidya Sagar  (11 years ago)

Let the two numbers be x and y
Their sum is 20 ---> x + y = 20 .... (1)
AM = (x+y)/2 and GM = √xy
Their GM is 20% less than their AM
 (x+y)/2-(x+y)/10=√xy
⇒ 4(x+y)/10=√xy
⇒(4×20)/10=√xy
⇒8=√xy
⇒xy=64
(x-y)^2=(x+y)^2-4xy
⇒(x-y)^2=400-256
⇒(x-y)^2=144
 x – y = 12 ………… (2)
Solving equations (1) and (2)
We get x = 16 and y = 4
Two numbers are 16 and 4.

Is this solution Helpfull? Yes (12) | No (3)  

MohanRaj  (11 years ago)

a+b = 20
(a+b)/2 = 10
ab = 8^2 = 64
a,b = 16,4 or 4,16
see options --> 4:1

Is this solution Helpfull? Yes (9) | No (5)  

Paresh  (11 years ago)

1 more method.....
Sum of both numbers is 20
So if one is x, then the other is (20-x).......... (1)
GM = SQRT ((20-x).x)....... (2)
AM = 1/2 (20) = 10.......... (3)

Now , GM is 20% lower than AM ... which means GM is 80% of AM
GM = 80% of 10 = 8 ..... from (3)

So, 8 = SQRT ((20-x).x)... from (2) & above
Squaring both sides, we get quadratic equation as follows:
x ^2 - 20x + 64 = 0
Solving, we get values as 16 & 4
Ratio is 4:1... so answer = 1

Is this solution Helpfull? Yes (5) | No   

nitu kumari  (10 years ago)

ans is 4:1
suppose the numbers are 16 and 4. their sum is 20 and arithmetic mean is 10 and GM is 8 and by solving the we get that gm is 205 less than am

Is this solution Helpfull? Yes (1) | No   

Anilkumar  (11 years ago)

x=16,y=4,
Ans.1) 4:1
G.M=(16*4)^1/2=8,
A.M=16+4/2=10,
G.M is 20% lower than A.M
Therefore,ratio is 16/4=4:1

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Debasish Roy  (11 years ago)

Let the ratio is k:1, one is kx other x.
Therefore (kx+x)=20(This condition is redundant)
((kx+x)/2)*(4/5)= sqrt.k*x
2k - 5*sqrt.k+2=0 This implies sqrt.k=2or1/2. That is k:1=4:1 or 1:4

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sagar  (10 years ago)

Ans is 4:1

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sravani  (9 years ago)

4:1 is the ratio and the numbers are 16 and 4.
These satisfies all the conditions mentioned.

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