$If a : b = 3 : 4 and b : c = 5 : 9 then a : b : c is.$

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15: 20: 36

20: 36: 15

3: 20: 9

None of these

answer is A.

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Detailed Solution

Given that,
a: b = 3: 4 and,
b: c = 5: 9……. (i)
The matching values for b are 4 and 5, so we must get the LCM of those two numbers. Since 4 and 5 don't have a common factor, we must also find the LCM of those two numbers.

LCM (4, 5) = 4 \times 5 = 20

It is now necessary to adjust the above ratios so that 20 is the combination for b.
Here, we have,

\begin{matrix} a : b = 3 : 4 \\ \Rightarrow \frac{a}{b} = \frac{3}{4} \end{matrix}

Now, we must multiply the fractions by five in order to modify the denominator to 20.
We get,

\begin{matrix} \frac{a}{b} = \frac{3 \times 5}{4 \times 5} \\ \Rightarrow \frac{a}{b} = \frac{15}{20} \\ So, a : b = 15 : 20 \dots . . (ii) \end{matrix}

Now other ratio,

\frac{b}{c} = \frac{5}{9}

Now, divide and multiply by 4 in right hand side,

\begin{matrix} \frac{b}{c} = \frac{5 \times 4}{9 \times 4} \\ \frac{b}{c} = \frac{20}{36} \end{matrix}

Thus, we get,

b : c = 20 : 36

……. (iii)
Now, from equation (ii) and (iii) we get,

a : b : c = 15 : 20 : 36

(as b=20 is common in both)
Hence, correct option is 1.

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