SSC CGL Tier II 25 Oct 2015 Paper 1

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Question : 76 of 100

Marks: +1, -0

If

(x^{3}-y^{3} ) : (x^{2}+x y+y^{2} )=5 : 1

and

(x^{2}-y^{2} ) :(x-y)=7 : 1

then the ratio

2x : 3y

equals

4 : 1
2 : 3
4 : 3
3 : 2

Solution:

(1)

{x^{3}-y^{3}}/{x^{2}+x y+y^{2}}= {5}/{1}

⇒{(x-y) (x^{2}+x y+y^{2} )}/{x^{2}+x y+y^{2}}=5

⇒ x-y=5....(i)

Again,

{x^{2}-y^{2}}/{x-y}=7

⇒{(x+y)(x-y)}/{x-y}=7

⇒ x+y=7....(ii)

On adding equations (i) and (ii),
2x = 12 ⇒ x = 6
From equation (ii),
x + y = 7 ⇒ y = 7 – 6 = 1
∴

{2 x}/{3 y}= {2×6}/{3 × 1}=4 : 1

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