If 4a - 18b + 13c = 0 and 3a + 3b - 4c = 0 then the ratio a : b : c will be

3 : 6 : 5

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5 : 3 : 6

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3 : 5 : 6

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5 : 6 : 3

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Solution

The correct option is C $3 : 5 : 6$
Given,
$4 a - 18 b + 13 c = 0$ (i)
$3 a + 3 b - 4 c = 0$ (ii)
$=> \frac{a}{(- 18) \times (- 4) - 3 \times 13} = \frac{b}{13 \times 3 - (- 4) \times 4} = \frac{c}{4 \times 3 - 3 \times (- 18)}$
$=> \frac{a}{72 - 39} = \frac{b}{39 + 16} = \frac{c}{12 + 54}$
$=> \frac{a}{33} = \frac{b}{55} = \frac{c}{66}$
$=> \frac{a}{3} = \frac{b}{5} = \frac{c}{6} = x (s a y)$ [multiplying by each term by $11$ ]
$=> a = 3 x, b = 5 x, c = 6 x$
So,
$a : b : c = 3 x : 5 x : 6 x$
$= 3 : 5 : 6$
$∴ a : b : c = 3 : 5 : 6$

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