The value of $x$ is ____ if $(3 x + 1) : (5 x - 4)$ is the duplicate ratio of $5 : 6$

2

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4

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8

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6

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Solution

The correct option is C $8$
$(3 x + 1) : (5 x - 4)$ is the duplicate ratio of $5 : 6$ .
Also, the duplicate ratio of $5 : 6$ is $5^{2} : 6^{2} = 25 : 36$
$∴ \frac{3 x + 1}{5 x - 4} = \frac{25}{36}$
$∴ 108 x + 36 = 125 x - 100$
$∴ 125 x - 108 x = 36 + 100$
$∴ 17 x = 136$
$∴ x = \frac{136}{17} = 8$

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