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Find the rati...

Question

Find the ratio compounded of the three ratios: $2 a : 3 b, a b : 5 c^{2}, c : a$

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Solution

Given $2 a : 3 b$ and $a b : 5 c^{2}$ and $c : a$
$2 a^{2} : 3 a b$ and $3 a b : 15 c^{2}$ and $3 b c : 3 a b$
$\frac{2 a^{2}}{3 a b} : \frac{3 a b}{15 c^{2}} : \frac{3 b c}{3 a b}$
$∴ 2 a^{2} : 15 c^{2} : 3 b c$

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Similar questions

Q. Find the ratio compounded of
(1) the ratio 2a, 3b, and the duplicate of

9 b^{2} : a b .

(2) the subduplicate ratio of 64 : 9, and the ratio 27 : 56.
(3) the duplicate ratio of

\frac{2 a}{b} : \frac{\sqrt{C} a^{2}}{b^{2}},

and the ratio 3ax : 2by .

\frac{a}{b} = \frac{7}{3}

then find the values of the following ratios.

\frac{3 a^{2} + 3 b^{2}}{2 a^{2} - 3 b^{2}}

2 a + 3 b - 5 c = 0

then prove that the points

A (¯ a), B (¯ b)

C (¯ c)

are collinear. Hence, find the ratio in which the point

C

divides the line segment

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¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

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2 ¯ ¯ ¯ a + 3 ¯ ¯ b - 5 ¯ ¯ c = ¯ ¯ ¯ 0

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where a > 0, b > 0, then find the minimum value of ab.

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