Let it take x hours to fill the tank by all the three pipes. Then,
Work done by {A in x hours + B in (x – 1) hours + C in (x – 2) hours} = 1
\(\Rightarrow\) \(\frac{X}{10}\) + \(\frac{(X-1)}{12}\)+ \(\frac{(X-2)}{15}\) = 1
\(\Rightarrow\) 6x + 5(x – 1) + 4(x – 2) = 60
\(\Rightarrow\) 15x – 13 = 60
\(\Rightarrow\) 15x = 73
\(\Rightarrow\) x = \(\frac{73}{15}\) = 4\(\frac{13}{15}\) = 4 hours + \(\frac{13}{15}\) x 60 min = 4 hours 52 min.