a) 30 days
b) 40 days
c) 60 days
d) 70 days

Answer: c
Explanation:
$$\eqalign{ & {\text{Let}}\,{\text{A’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = x\,{\text{and}} \cr & {\text{B’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = y \cr & {\text{Then}},\,x + y = \frac{1}{{30}} \cr & 16x + 44y = 1 \cr & {\text{Solving}}\,{\text{these}}\,{\text{two}}\,{\text{equations,}} \cr & x = \frac{1}{{60}}\,{\text{and}}\,y = \frac{1}{{60}} \cr & {\text{B’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = \frac{1}{{60}} \cr & {\text{Hence,}}\,{\text{B}}\,{\text{alone}}\,{\text{shall}}\,{\text{finish}}\,{\text{the}}\,{\text{whole}}\,{\text{work}}\,{\text{in}}\,{\text{60}}\,{\text{days}} \cr} $$