Na 4–hour examination of 420 questions, there are 60 mathematics problems. if twice as much time should be allowed for each mathematics problem as for each of the other questions, how many minutes should be spent on the mathematics problems?

The number of questions in the quiz is 420 questions.
Time allocated for the paper=4 hours
time for each question:
1/105
=1/105×60
=4/7 minutes
if twice as much time is given on Math the new amount of time for Math questions will be:
4/7×2=8/7 min
total number of time allocated for Math will be:
(total added time)×(number of questions)
8/7×60
=68 4/7 minutes
 

1 minute per math problem.

   This problem wants you to create and solve an equation. For instance, let's assign the variable x for the amount of time to spend on a non-math problem. Is so the equation is:
 (420-60)x + 2*60x = 4*60
 And solve for x, so:
 360x + 120x = 240
 480x = 240
 x = 240/480 = 1/2
 And since the math problems need twice as much time, you need 2*1/2 = 1 minute per math problem.

   Another way of solving the problem is to realize that if each math problem takes twice as much time, how about adding and extra set of "phantom" math problems and have them all take the same amount of time. So 4*60/(420+60) = 240/480 = 1/2. And then double the time to get 2*1/2 = 1 minute. Either way works.