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SSC MTS 2019 PYQ — Question 55

SSC MTS Previous Year - 07 August 2019 - Shift 1 • Quantitative Aptitude • Q55

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If X2 + Y2 = 100 and X : Y = 4 : 3, then what is the value of X2 - Y2 ?

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Correct answer: B

Explanation

Correct Answer is option 2 i.e. 28

Understanding

Application

Given:      

X2 + Y2 = 100 and

X : Y = 4 : 3

Suppose

X = 4a, Y = 3a

So,

(4a)2 + (3a)2 = 100

⇒ 16a2 + 9a2 = 100

⇒ 25a2 = 100

⇒ a2 = 4

 

Hence,

X2 – Y2

= 16a2 – 9a2

= 7a2

= 7 × 4 = 28