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\(\frac{1}{{a\: + \;\frac{1}{{b\: + \:\frac{7}{c}}}}} = \frac{{22}}{{37}}\) then a + b + c = ?1. 152. 223. 74. 17 |
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Answer» Correct Answer - Option 4 : 17 Given: \(\frac{1}{{a\: + \;\frac{1}{{b\: + \;\frac{7}{c}}}}} = \frac{{22}}{{37}}\) Calculation: \(\frac{{22}}{{37}} = \;\frac{1}{{37/22}}\) (on dividing by 22) \(\Rightarrow \frac{1}{{37/22}} = \;\frac{1}{{1\: +\: \frac{{15}}{{22}}}}\) \( \Rightarrow \frac{1}{{1\: + \:\frac{{15}}{{22}}}} = \;\frac{1}{{1\: + \;\frac{1}{{22/15}}}} = \;\frac{1}{{1\: + \;\frac{1}{{1\: + \;\frac{7}{{15}}}}}}\) \( \Rightarrow \frac{1}{{a\: + \;\frac{1}{{b \:+ \;\frac{7}{c}}}}} = \;\frac{1}{{1\: + \;\frac{1}{{1\: + \;\frac{7}{{15}}}}}}\) On comparing both side we get, a = 1, b = 1 and c = 15 ∴ a + b + c is 17. |
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