If A and B can finish a work in 10 days, B and C can finish the same work in 12 days, C and A can finish the same work in 15 days; then in how many days can A, B and C together finish half of the work?

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