If $$\frac{1}{{x + \frac{1}{{y + \frac{2}{{z + \frac{1}{4}}}}}}} = \frac{{29}}{{79}},$$    where x, y and z are natural numbers, then the value of (2x + 3y - z) is:

Solution (By Examveda Team)

$$\eqalign{ & \frac{1}{{x + \frac{1}{{y + \frac{2}{{z + \frac{1}{4}}}}}}} = \frac{{29}}{{79}} \cr & \frac{1}{{2 + \frac{1}{{1 + \frac{2}{{5 + \frac{1}{4}}}}}}} = \frac{{29}}{{79}} \cr & x = 2,\,y = 1,\,z = 5 \cr & \left( {2x + 3y - z} \right) \cr & = 2 \times 2 + 3 \times 1 - 5 \cr & = 2 \cr} $$