If x a y b 3 and x b ndash y a 9 then what is the value of x y ........

Quantitative Aptitude ( CCS) Algebra

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If (x/a) + (y/b) = 3 and (x/b) – (y/a) = 9, then what is the value of x/y?

(b + 3a) / (a – 3b)

(a + 3b) / (b – 3a)

(a + 3b²) / (b – 3a²)

(1 + 3a) / (a + 3b)

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Explanation:

Here (x/a) + (y/b) = 3
⇒ bx + ay – 3ab = 0 ---- (1)
Here (x/b) – (y/a) = 9
⇒ ax – by – 9ab = 0 ---- (2)
Multiplying equation 1 by ‘a’ and equation 2 by ‘b’
⇒ abx + a²y – 3a²b = 0 ---- (3)
⇒ abx – b²y – 9ab²= 0 ---- (4)
Subtracting equation 4 from 3,
⇒ y = 3ab(a – 3b) / (a² + b²),
substituting value of y in equation 3,
⇒ x = 3ab(b + 3a) / (a²+ b²)
⇒ x/y = (b + 3a) / (a – 3b)
∴ The value of x/y = (b + 3a) / (a – 3b)