Explanation:

Let the total work be 40 units.
$$(\because$$ L.C.M. of 10 and 40 is 40.)
Efficiency of A = work/time = 40/10 = 4 units/hour
Efficiency of B = 40/40 = 1 unit/hour
Time time taken by pipe A and B = $$\frac{40}{4+1}$$ = 8 hours
Time time taken by pipe A, B and C together = 8 hours + 80/60 hours = 28/3 hours
Efficiency of A, B and C together = $$\frac{40}{28/3}$$ = 30/7 units/hour
Efficiency of C alone = 30/7 - 5 = -5/7 (- as pipe C is an outlet pipe and does negative work)
Work done by pipe A and B in 7 hours = (1 + 4)$$\times$$7 = 35 units
Time taken by pipe C to empty the tank = $$\frac{35}{5/7}=49$$