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# If a/b=3/5 , then what is the value

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Founder
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If a/b=3/5 , then what is the value [#permalink]  04 Jun 2020, 09:33
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Question Stats:

75% (01:23) correct 25% (03:22) wrong based on 12 sessions
If $$\frac{a}{b}=\frac{3}{5}$$ , then what is the value $$\frac{b(a+b)(\frac{b}{a}-1)}{a(a-b)(\frac{a}{b}-1)}$$

[Reveal] Spoiler: OA
$$\frac{100}{9}$$

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Founder
Joined: 18 Apr 2015
Posts: 12104
Followers: 256

Kudos [?]: 3022 [0], given: 11294

Re: If a/b=3/5 , then what is the value [#permalink]  04 Jun 2020, 09:33
Expert's post
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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Manager
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Re: If a/b=3/5 , then what is the value [#permalink]  04 Jun 2020, 20:23
Can anybody explain?
Intern
Joined: 18 May 2020
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Re: If a/b=3/5 , then what is the value [#permalink]  04 Jun 2020, 20:56
3
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Carcass wrote:
If $$\frac{a}{b}=\frac{3}{5}$$ , then what is the value $$\frac{b(a+b)(\frac{b}{a}-1)}{a(a-b)(\frac{a}{b}-1)}$$

[Reveal] Spoiler: OA
$$\frac{100}{9}$$

Divide the numerator and denominator by ab

$$\frac{\frac{b(a+b)}{ab}(\frac{b}{a}-1)}{\frac{a(a-b)}{ab}(\frac{a}{b}-1)}$$

$$\frac{\frac{(a+b)}{a}(\frac{b}{a}-1)}{\frac{(a-b)}{b}(\frac{a}{b}-1)}$$

$$\frac{(1+\frac{b}{a})(\frac{b}{a}-1)}{(\frac{a}{b}-1)(\frac{a}{b}-1)}$$

$$\frac{(\frac{b}{a}+1)(\frac{b}{a}-1)}{(\frac{a}{b}-1)(\frac{a}{b}-1)}$$

$$\frac{(\frac{b}{a})^2-1}{(\frac{a}{b}-1)^2}$$

Now substitute the value a/b=2/5 and b/a = 5/3

$$\frac{(\frac{5}{3})^2-1}{(\frac{3}{5}-1)^2}$$

$$\frac{\frac{25}{9}-1}{(\frac{-2}{5})^2}$$

$$\frac{\frac{16}{9}}{\frac{4}{25}}$$

$$(\frac{16}{9})(\frac{25}{4})$$

$$\frac{100}{9}$$
Founder
Joined: 18 Apr 2015
Posts: 12104
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Kudos [?]: 3022 [0], given: 11294

Re: If a/b=3/5 , then what is the value [#permalink]  05 Jun 2020, 09:10
Expert's post
Great Job
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Re: If a/b=3/5 , then what is the value   [#permalink] 05 Jun 2020, 09:10
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