CAT Exam Numerical Ability Time and Work

A tap can fill a tank in 6hrs. after half the tank is filled, three more similar taps are opened. what is the total time taken to fill the tank completely?

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CAT Other Question

A pipe can fill a tank in 16hrs.due to a leak in the bottom of the tank it is filled in 24hrs. if the tank is full. how much time will the leak take to empty it? Two pipes a and b can separetly fill a cistern in 60min and 75min respectively. there is a third pipe in the bottom of the cistern to empty it. if all the three pipes are simultaneously opened, then the cistern is full in 50min. in how much time the third pipe alone can empty the cistern?