If 0.04×0.4×a=0.4×0.04×b then find the ratio ab. - Algebra

If `sqrt(0.04 xx 0.4 xx a ) = 0.4 xx0.04 xx sqrtb` then find the ratio `a/b`.

Sum

`sqrt(0.04 xx 0.4 xx a) = 0.4 xx0.04 xx sqrtb`

Squaring both sides,

`(sqrt(0.04 xx 0.4 xx a))^2 = (0.4 xx0.04 xx sqrtb)^2`

∴ `0.04 xx 0.4 xx a = 0.4^2 xx0.04^2 xx sqrtb^2`

∴ `0.04 xx 0.4 xx a = 0.4^2 xx0.04^2 xx b`

∴ `a/b = (0.4 xx 0.4 xx 0.04 xx 0.04)/(0.04 xx 0.4)`

∴ `a/b = 0.4 xx 0.04`

= `4/10 xx 4/100`

= `2/5 xx 1/25`

= `a/b = 2/125`

`therefore` a : b = 2 : 125

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Comparison of Ratios

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Chapter 4: Ratio and Proportion - Practice Set 4.2 [Page 64]

Chapter 4 Ratio and Proportion
Practice Set 4.2 | Q (6) | Page 64

Using the property `bb("a"/"b" = ("ak")/("bk"))`, fill in the blanks substituting proper numbers in the following.

`5/7 = ("___")/28 = 35/("___") = ("___")/3.5`

Using the property `bb(a/b = (ak)/(bk))`, fill in the blanks substituting proper numbers in the following.

`9/14 = 4.5/("___") = ("___")/ 42 = ("___") /3.5`