Discussion

If X : Y = 9 : 11, then the value of \(\dfrac{5x + 3y}{3x + 5y}\) is :

Answer: D

The value is 39 : 41.

Put \(x = 9k\) and \(y = 11k\); the \(k\) cancels:

\[ \begin{aligned} \frac{5(9) + 3(11)}{3(9) + 5(11)} &= \frac{45 + 33}{27 + 55} \\ &= \frac{78}{82} = \frac{39}{41} \end{aligned} \]

45 : 55 and 18 : 22 are just multiples of 9 : 11, as if the expression did not change the ratio, and 37 : 41 is an arithmetic slip.

The case of the letters (X : Y in the ratio, x and y in the expression) is a printing inconsistency; both refer to the same two quantities.

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