Find the :

(i) duplicate ratio of $2 \sqrt{2} : 3 \sqrt{5}$

(ii) triplicate ratio of 2a : 3b,

(iii) sub- duplicate ratio of $9 x^{2} a^{4} : 25 y^{6} b^{2}$

(iv) sub-triplicate ratio of 216 : 343

(v) reciprocal ratio of 3 :5

(vi) ratio compounded of the duplicate ratio of 5 :6, the reciprocal ratio of 25 : 42 and the sub - duplicate ratio of 36 : 49.

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Solution

$left parenthesis i right parenthesis D u p l i c a t e space r a t i o space o f space 2 square root of 2 colon 3 square root of 5 equals left parenthesis 2 square root of 2 right parenthesis squared colon left parenthesis 3 square root of 5 right parenthesis squared equals 8 colon 45 left parenthesis i i right parenthesis T r i p l i c a t e space r a t i o space o f space 2 a colon 3 b equals open parentheses 2 a close parentheses cubed colon left parenthesis 3 b right parenthesis cubed equals 8 a cubed colon 27 b cubed left parenthesis i i i right parenthesis S u b minus d u p l i c a t e space r a t i o space o f space 9 x squared a to the power of 4 colon 25 y to the power of 6 b squared equals square root of 9 x squared a to the power of 4 end root colon square root of 25 y to the power of 6 b squared end root equals 3 x a squared colon 5 y cubed b left parenthesis i v right parenthesis S u b minus t r i p l i c a t e space r a t i o space o f space 216 colon 343 space equals cube root of 216 colon cube root of 343 equals 6 colon 7 left parenthesis v right parenthesis R e c i p r o c a l space r a t i o space o f space 3 colon 5 equals 5 colon 3 left parenthesis v i right parenthesis D u p l i c a t e space r a t i o space o f space 5 colon 6 equals 25 colon 36 r e c i p r o c a l space r a t i o space o f space 25 colon 42 equals 42 colon 25 S u b minus d i p l i c a t e space r a t i o space o f space 36 colon 49 equals 6 colon 7 r e q u i r e d space c o m p o u n d space r a t i o space equals fraction numerator 25 cross times 42 cross times 6 over denominator 36 cross times 25 cross times 7 end fraction equals 1 colon 1$

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Similar questions

Find the ratio compounded of the reciprocal ratio of 15 : 28, the sub -duplicate ratio of 36 : 49 and the triplicate ratio of 5 :4.

5 : 6

25 : 42

216 : 343

(v i)

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