In two days A, B and C together can finish $$\frac{1}{2}$$ of a work and in another 2 days B and C together can finish $$\frac{3}{{10}}$$ part of the work. Then A alone can complete the whole work in ?
a) 15 days
b) 10 days
c) 12 days
d) 14 days

Answer: b
Explanation:
$$\eqalign{ & \frac{3}{{10}}\left( {{\text{B}} + {\text{C }}} \right) = 2{\text{ days}} \cr & \left( {{\text{B}} + {\text{C }}} \right) = 2 \times \frac{{10}}{3} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{3}{\text{ days}} \cr & \frac{1}{2}\left( {{\text{A}} + {\text{B}} + {\text{C }}} \right) = 2{\text{ days}} \cr & {\text{A}} + {\text{B}} + {\text{C}} = {\text{4 days}} \cr} $$
L.C.M of total work = 20
One day work of A + B + C = $$\frac{{20}}{4}$$ = 5 unit/day
One day work of B + C = $$\frac{{20}}{{\frac{{20}}{3}}}$$ = 3 unit/day
A = 5 – 3 = 2
A alone will complete the work
$$\eqalign{ & = \frac{{20}}{2}{\text{days}} \cr & = {\text{10 days}} \cr} $$