Question

If A:B= 5:8 and B: C =
18:05, then find A:B:C​

Answer 1

Given

A:B = 5:8

B:C = 18:5

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To Find

A:B:C

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Solution

In the ratio, A:B and B:C they have a common value, 'B'.

So now we would find the LCM of the value of 'B' in both ratios.

$\begin{array}{r | l} 2 & 8,18\\ \cline{2-2} 2 & 4,9 \\ \cline{2-2} 2 & 2,9 \\ \cline{2-2} 3& 1,9 \\ \cline{2-2} 3 & 1,3 \\ \cline{2-2} & 1,1\\ \end{array}$

LCM of 8 and 18 ⇒ 2 × 2 × 2 × 3 × 3 = 72

A:B ⇒ $\dfrac{5}{8}$ ⇒ $\dfrac{5\times 9 }{8\times 9} =\dfrac{45}{72}$

B:C ⇒ $\dfrac{18}{5}$ ⇒ $\dfrac{18\times 4 }{5 \times 4 } = \dfrac{72}{20}$

A:B:C ⇒ 45:72:20

∴ A : B : C = 45:72:20

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Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

• If A : B= 5 : 8 and B : C =  18 : 05, then find A : B : C​

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♣ ᴀɴꜱᴡᴇʀ :

A short trick to solve such problems :

Now in our question :

A : B= 5 : 8

B : C = 18 : 05

A : B = 5 : 8

             \/  \        

B : C =   18 : 5

A : B : C = 5 × 18 : 18 × 8 : 8 × 5

A : B : C = 90 : 144 : 40

When Brought to lowest terms :

A : B : C = 45 : 72 : 20