Answer
Work done by A and B in one day = $$\frac{1}{10}$$
Work done by B and Cin one day = $$\frac{1}{12}$$
Work done by C and A in one day = $$\frac{1}{15}$$
$$\frac{1}{A} + \frac{1}{B}= \frac{1}{10}$$ ———-(a)
$$\frac{1}{B} + \frac{1}{C}= \frac{1}{12}$$ ———-(b)
$$\frac{1}{C} + \frac{1}{A} = \frac{1}{15}$$ ———-(c)
On adding a,b, and c,
$$2\left(\frac{1}{A} + \frac{1}{B}+\frac{1}{C}\right) = \frac{1}{10} +\frac{1}{12} + \frac{1}{15}$$
$$\left(\frac{1}{A} + \frac{1}{B}+\frac{1}{C}\right) = \frac{1}{8}$$
Total work is finished in 8 days. So, half of the work is finished in 4 days.
Answer (C) ⇒ 4 days