Study the following graph and answer the given questions.

The graph shows the time(in minutes) takes by the pipe (A,B), (C, D), (E, F), (G, H) and (P, Q) to fill a tank.

In how many minutes is an empty tank filled completely if pipe D fills it for half the time and then for the other half time, pipes C and D fill it together?

12 minutes

Time taken by D to fill the tank = 20 minutes

D fill the tank for half of the time .

Let total time take to fill the tank = T

Work done by D in one minute = \(\frac{1 }{20 }\)

Work done by D alone to fill first half ,

= \(\frac{T }{2}\) × \(\frac{1 }{20 }\) 

= \(\frac{T }{40}\) 

Now ,

Time taken by C to fill the tank = 15 minutes

Work done by C  in one minute = \(\frac{1 }{15 }\) 

When C and D works together = \(\frac{1 }{15 }\) + \(\frac{1 }{20 }\) 

= \(\frac{7}{60 }\) 

Work done by C and D together to fill rest half ,

= \(\frac{T }{2}\) × \(\frac{7 }{60 }\) 

= \(\frac{7T }{120}\)

Now ,

\(\frac{T }{40}\)  + \(\frac{7T }{120}\)  = 1

T = 12 minutes