Determine the Winner

There is a contest containing
2
2 problems

A and

B.

2
2 strong participants

P and

Q participated in the contest and solved both the problems.

P made AC submissions on problems

A and

B at time instants


P
A

and


P
B

respectively while

Q made AC submissions on problems

A and

B at time instants


Q
A

and


Q
B

.

It is given that the time penalty is the minimum time instant at which a participant has solved both the problems. Also the participant with the lower time penalty will have a better rank.

Determine which participant got the better rank or if there is a TIE.

why in the solution there is maximum of two chosen ,though the question says minimum time