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Changing Scale (Including Flags)

If p : q = r ...

Question

If p : q = r : s = t : u = 2 : 3 then what is (mp + nr + ot) : (mq + ns + ou) equal to?

2 : 3

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5 : 6

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7 : 9

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2 : 5

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Solution

The correct option is A 2 : 3
Given $p : q = r : s = t : u = 2 : 3$

$⟹ \frac{p}{q} = \frac{r}{s} = \frac{t}{u} = \frac{2}{3}$

Let $p = r = t = 2 x$ and $q = s = u = 3 x$

Then $\frac{m p + n r + o t}{m q + n s + o u} = \frac{m \times 2 x + n \times 2 x + o \times 2 x}{m \times 3 x + n \times 3 x + o \times 3 x} = \frac{2 x (m + n + o)}{3 x (m + n + o)} = \frac{2}{3} = 2 : 3$

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