Find the compound ratio of :

(i) 2 : 3, 9 : 14 and 14 : 27.

(ii) 2a : 3b, mn : $x^{2}$ and x : n.

(iii) $\sqrt{2}$ : 1, 3 : $\sqrt{5}$ and $\sqrt{20} : 9$ .

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Solution

$left parenthesis i right parenthesis R e q u i r e d space c o m p o u n d space r a t i o equals 2 cross times 9 cross times 14 colon 3 cross times 14 cross times 27 equals fraction numerator 2 cross times 9 cross times 14 over denominator 3 cross times 14 cross times 27 end fraction equals 2 over 9 equals 2 colon 9 left parenthesis i i right parenthesis R e q u i r e d space c o m p o u n d space r a t i o equals 2 a cross times m n cross times x colon 3 b cross times x squared cross times n equals fraction numerator 2 a cross times m n cross times x over denominator 3 b cross times x squared cross times n end fraction equals fraction numerator 2 a m over denominator 3 b x end fraction equals 2 a m colon 3 b x left parenthesis i i i right parenthesis R e q u i r e d space r a t i o equals square root of 2 cross times 3 cross times square root of 20 colon 1 cross times square root of 5 cross times 9 equals fraction numerator square root of 2 cross times 3 cross times square root of 20 over denominator 2 cross times square root of 5 cross times 9 end fraction equals fraction numerator square root of 2 cross times square root of 4 over denominator 3 end fraction equals fraction numerator 2 square root of 2 over denominator 3 end fraction 2 square root of 2 colon 3$

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Similar questions

Find the value of $27 x^{3} + 8 y^{3}$ , if

(i) 3x + 2y = 14 and xy = 8

(ii) 3x + 2y = 20 and xy = $\frac{14}{9}$

If $3 x + \frac{1}{3 x} = 3; f i n d : (i) 9 x^{2} + \frac{1}{9 x^{2}} (i i) 27 x^{3} + \frac{1}{27 x^{3}}$

(i)

2 : 3, 9 : 14 and 14 : 27

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