Question

If \(a:b=\frac{2}{3}:\frac{1}{4}\) and \(b:c=\frac{3}{4}:\frac{4}{5}\) then find a : b : c.

• A. 20 : 8 : 15
• B. 20 : 16 : 15
• C. 40 : 15 : 12
• D. 40 : 15 : 16

Answer 1

The Correct Option is D

To find the combined ratio \(a:b:c\), we first calculate each given ratio:

Step 1: Simplify the ratio \(a:b = \frac{2}{3}:\frac{1}{4}\).

\(\frac{a}{b} = \frac{\frac{2}{3}}{\frac{1}{4}} = \frac{2}{3} \times \frac{4}{1} = \frac{8}{3}\)

Thus, \(a:b = 8:3\).

Step 2: Simplify the ratio \(b:c = \frac{3}{4}:\frac{4}{5}\).

\(\frac{b}{c} = \frac{\frac{3}{4}}{\frac{4}{5}} = \frac{3}{4} \times \frac{5}{4} = \frac{15}{16}\)

Thus, \(b:c = 15:16\).

Step 3: Combine the ratios.

\(a:b = 8:3\) and \(b:c = 15:16\).

To combine them, the 'b' values must match. Compute the LCM of 3 and 15, which is 15.

Convert \(a:b\), maintaining the ratio:
\(a:b = 8:3\Rightarrow 8 \times 5:3 \times 5 = 40:15\).

The second ratio is already \(b:c = 15:16\).

Step 4: Combine to find \(a:b:c\).

The unified ratio is \(a:b:c = 40:15:16\).

Thus, the combined ratio \(a:b:c\) is \(\mathbf{40:15:16}\).