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)?

A. 6

B. 4

C. 5

D. 7

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \frac{{45}}{{53}} = \frac{1}{{a + \frac{1}{{b + \frac{1}{{c - \frac{2}{5}}}}}}} \cr & \frac{{53}}{{45}} = 1 + \frac{8}{{45}},\,\frac{{45}}{8} = 5 + \frac{5}{8},\,\frac{8}{5} = 2 - \frac{2}{5} \cr & a = 1 \cr & b = 5 \cr & c = 2 \cr & 4a - b + 3c \cr & = 4 \times 1 - 5 + 3 \times 2 \cr & = 4 - 5 + 6 \cr & = 5 \cr} $$