Pipe X takes 6 hours to fill a cistern and another pipe Y takes 7 and half hours to fill the same cistern. If the pipes X and Y are switched together at the same time and X is closed after 1 and half hours then the extra time taken by Y to fill the cistern is -

X takes 6 hours, part filled by X in 1 hour = 1/6
Y takes 7(1/2) hours, part filled by Y in 1 hour = 1/7.5 or 2/15.
Therefore, the part filled by X and Y together = 1/6 + 2/15
X and Y together fill the cistern for 1(1/2) hour = 3/2 hours.
Part filled by (X + Y) in 3/2 hours = (3/2)(1/6 + 2/15) = (3/2)(3/10) = 9/20
Remaining part filled by Y alone = 1 - 9/20 = 11/20.
Part Filled Time Taken by Y(2/15) hr. = 1 hour
Time taken to fill (11/20) part by Y alone = (11/20)/(2/15)
= 11/20 x 15/2
= 33/8 hours.