If (a + 3b) : (2a + 4b) = 3 : 5, then (a - b) : (a + b) is equal to:

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SSC GD Constable Memory Based Test (11 Jan 2023 Shift 1)

Answer 1

Given:

(a + 3b) : (2a + 4b) = 3 : 5

Formula used:

if \(\frac{a}{b} = \;\frac{c}{d}\)

then, \(\;\;\frac{{a - b}}{{a + b}} = \;\frac{{c - d}}{{c + d}}\)

Calculation:

\(\frac{{\left( {a + 3b} \right)}}{{\left( {2a + 4b} \right)}} = \;\frac{3}{5}\)

⇒ 5 × (a + 3b) = 3 × (2a + 4b)

⇒ 5a + 15b = 6a + 12b

⇒ a = 3b

⇒ \(\frac{a}{b} = \;\frac{3}{1}\)

⇒ \(\frac{{a - b}}{{a + b}} = \;\frac{{3 - 1}}{{3 + 1}}\)

⇒ \(\frac{{a - b}}{{a + b}} = \;\frac{2}{4} = \;\frac{1}{2}\)

⇒ (a - b) : (a + b) = 1 : 2

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