If $(4 x + 3) : (9 x + 10)$ is the triplicate ratio of $3 : 4$ , then the value of x is ___

6

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12

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5

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4

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Solution

The correct option is D $6$
The triplicate ratio of $3 : 4$ is $3^{3} : 4^{3} = 27 : 64$
$∴ \frac{4 x + 3}{9 x + 10} = \frac{27}{64}$
$\Rightarrow 256 x + 192 = 243 x + 270$
$\Rightarrow 256 x - 243 x = 270 - 192$
$\Rightarrow 13 x = 78$
$\Rightarrow x = \frac{78}{13} = 6$
$\Rightarrow x = 6$

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