If \(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \f

1.	If \(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}},\) where a, b and c are positive integers, then what is the value of (4a - b + 3c)1. 62. 43. 74. 5
Answer» Correct Answer - Option 4 : 5 Calculations: \(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}}\) \( \) \(⇒ \frac{1}{{1 \; + \;\frac{8}{{45}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\) \(⇒ \frac{1}{{1\; + \;\frac{1}{{5\; + \;\frac{5}{8}}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\) \(⇒ \frac{1}{{1\; + \;\frac{1}{{5\; + \;\frac{1}{{2 \;- \;\frac{2}{5}}}}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\) Compare both the sides ⇒ a = 1, b = 5 and c = 2 Value of (4a – b + 3c) = 4 × 1 – 5 + 3 × 2 ⇒ 10 – 5 = 5 ∴ The value of 4a – b + 3c is 5

If \(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}},\) where a, b and c are positive integers, then what is the value of (4a - b + 3c)1. 62. 43. 74. 5

Answer» Correct Answer - Option 4 : 5

Calculations:

\(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}}\)

\( \)
\(⇒ \frac{1}{{1 \; + \;\frac{8}{{45}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\)

\(⇒ \frac{1}{{1\; + \;\frac{1}{{5\; + \;\frac{5}{8}}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\)

\(⇒ \frac{1}{{1\; + \;\frac{1}{{5\; + \;\frac{1}{{2 \;- \;\frac{2}{5}}}}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\)

Compare both the sides

⇒ a = 1, b = 5 and c = 2

Value of (4a – b + 3c) = 4 × 1 – 5 + 3 × 2

⇒ 10 – 5 = 5

∴ The value of 4a – b + 3c is 5

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