If x varies as y then x2 + y2 varies as
A. x + y
B. x - y
C. x2 - y2
D. x3 - y3
E. None of these
Answer: Option E
Solution(By Examveda Team)
Given,x = y Or, x - y = 0 Or, (x - y)2 = 0
Or, x2 + y2 - 2xy = 0 Or, x2 + y2 = 2xy
It means that, x2 + y2 varies as xy
This Question Belongs to Arithmetic Ability >> Ratio
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Comments ( 4 )
Related Questions on Ratio
If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : c is equal to
A. 2 : 1
B. 14 : 3
C. 7 : 2
D. 1 : 2
If $$\frac{2}{3}$$ of A=75% of B = 0.6 of C, then A : B : C is
A. 2 : 3 : 3
B. 3 : 4 : 5
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The answer is c
If x proportional to y then,
x=ky(where k is proportionality constant
x/y=k
x²/y²=k²
x²+y²/x²-y²=k²+1/k²-1 (componendo Dividendo)
x²+y²=(k²+1/k²-1)(x²-y²)
I.e. x²+y² is proportional to x²-y² where k²+1/k²-1 is new proportionality constant
@Onno Jogot : Yes , you are correct.
Btw, (x2 + y2) is proportional to y2 means, (x2 + y2) varies with y2.
In the answer they wrote x=y. It kind of confuses me. I think it should be x is proportional to y.
Thus,we can write:
x= ky [ where, k is a constant ]
Therefore, x2 + y2
= k2y2 + y2 [ since x= ky]
= y2 * (k2+1)
Therefore, x2 + y2 is proportional to y2, since (k2+1) is a constant.
The answer will be E.
Thanks.