NIFT UG 2020 Question Paper with solutions

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Question : 29 of 150

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

2 x: 3 y

equals

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

Solution:

Given,

\;{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}/{1}

⇒ \;\; x-y=5

.....(i)
and

\;\; \;{x^{2}-y^{2}}/{x-y}=\;{7}/{1}

⇒ \;\; x+y=7

.....(ii)
From Eqs. (i) and (ii), we get

x=6, y=1

∴

Required ratio

=2 x: 3 y

=2 × 6: 3 × 1

=12: 3=4: 1

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