1.

\(\frac{1}{{a\: + \;\frac{1}{{b\: + \:\frac{7}{c}}}}} = \frac{{22}}{{37}}\) then a + b + c = ?1. 152. 223. 74. 17

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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