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
Correct Answer: 48
Solution :
Given: Third proportion to 10 and X = 90
⇒ 10 : X : : X : 90
⇒ $\frac{10}{X} = \frac{X}{90}$
⇒ $X = \sqrt{10 \times 90} = 30$
Similarly, the third proportion to 12 and Y = 27
⇒ 12 : Y : : Y : 27
⇒ $\frac{12}{Y} = \frac{Y}{27}$
⇒ $Y = \sqrt{12 \times 27} = 18$
Therefore, the value of (X + Y) = 30 + 18 = 48
Hence, the correct answer is 48.
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