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If 2 p/3 p=4 ...

Question

If $\frac{2 p}{3 p} = \frac{4 k}{6 k} = \frac{2 p + 8 q}{3 p + 12 q}$ , then the value of k is .

A

4 q

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B

3 q

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C

2 q

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D

q

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Solution

The correct options are
A $4 q$
C $2 q$
As per the theorem of equivalent ratios in the more generalised form,

$\frac{a l}{b l}$ = $\frac{c m}{d m}$ = $\frac{a l + c m}{b l + d m}$

Hence,
$\frac{2 p}{3 p}$ = $\frac{4 k}{6 k}$ = $\frac{2 p + 4 k}{3 p + 6 k}$ = $\frac{2 p + 8 q}{3 p + 12 q}$
Equating we get,

$⟹ 4 k = 8 q$
$k = 2 q$

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