Question
Download Solution PDFIf \(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}},\) where a, b and c are positive integers, then what is the value of (4a - b + 3c)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculations:
\(\frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}}\)
\(⇒ \frac{1}{{1 \; + \;\frac{8}{{45}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\)
\(⇒ \frac{1}{{1\; + \;\frac{1}{{5\; + \;\frac{5}{8}}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\)
\(⇒ \frac{1}{{1\; + \;\frac{1}{{5\; + \;\frac{1}{{2 \;- \;\frac{2}{5}}}}}}} = \frac{1}{{a\; +\; \frac{1}{{b\;+ \;\frac{1}{{c\; -\; \frac{2}{5}}}}}}}\)
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
Last updated on Jun 13, 2025
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