Question : If the third proportion of 3 and $x$ is 27 and the third proportion of 2 and $y$ is 8, then find $x : y$.
Option 1: 7 : 9
Option 2: 4 : 5
Option 3: 3 : 7
Option 4: 9 : 4
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Correct Answer: 9 : 4
Solution : If c is called the third proportional to a and b, then a : b = b : c The third proportion of 3 and $x$ is 27. So, $\frac{3}{x}=\frac{x}{27}$ $⇒x=\sqrt{3×27}$ $\therefore x = 9$ The third proportion of 2 and $y$ is 8. So, $\frac{2}{y}=\frac{y}{8}$ $⇒y=\sqrt{2×8}$ $\therefore y = 4$ So, $x:y=9:4$ Hence, the correct answer is 9 : 4.
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Question : If the third proportion to 10 and X is 90 and the third proportion of 12 and Y is 27. Find the value of (X + Y).
Option 1: 56
Option 2: 44
Option 3: 48
Option 4: 50
Question : If $\mathrm{X: Y=3: 2}$, then what is the value of $\mathrm{(X-Y):(X+Y) }$?
Option 1: 4 : 5
Option 2: 1 : 5
Option 3: 8 : 9
Option 4: 3 : 7
Question : If $(3x+y):(3 x-y)=4: 3$, then what is the value of $x: y$?
Option 1: 5 : 3
Option 2: 7 : 3
Option 3: 5 : 2
Option 4: 7 : 4
Question : If (x + y) : (y + z) : (z + x) = 3 : 5 : 7 and (x + y + z) = 45, then what is the value of z?
Option 1: 18
Option 2: 30
Option 3: 27
Option 4: 20
Question : If $(7 x+y):(7 x–y)=7: 2$, then what is the value of $x: y$?
Option 1: 9 : 35
Option 2: 11 : 42
Option 3: 6 : 41
Option 4: 17 : 52
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