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  1. If (x + y - 8)/2 = (x + 2y - 14)/3 = (3x + y - 12)/11 then find the values of x and y, respectively.
    1. 2, 6
    2. 4, 8
    3. 3, 5
    4. 4, 5
    5. None of the above
Correct Option: A

Given,
(x + y - 8)/2 = (x + 2y - 14)/3 = (3x + y - 12)/11
⇒ (x + y - 8)/2 = (x + 2y - 14)/3
⇒ 3x + 3y - 24 = 2x + 4y - 28
⇒ 3x + 3y - 2x - 4y = -28 + 24
x - y = -4 ...(i)

Again, (x + 2y - 14)/3 = (3x + y - 12)/11
⇒ 11x + 22y - 154 = 9x + 3y - 36
⇒ 2x + 19y = 118 ..(ii)


On multiplying Eq. (i) by 2 and subtracting from Eq., we get
2x - 2y = -8
2x + 19y = 118
-------------------
-21y = -126
∴ y = 6

On putting the value of y in Eq. (i), we get
x - 6 = -4
∴ x = 2
∴ x = 2 and y = 6



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