Quantitative Aptitude - Arithmetic Ability Questions

Let there be x pupils in the class.

Total increase in marks = (x * 1/2) = x/2.

x/2 = (83 - 63) => x/2 = 20 => x = 40.

Average of 20 numbers = 0. 

Sum of 20 numbers = (0 * 20) = 0. 

It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a).

In this type of problems the formuae is
(5*x+ or - t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart

  Case 1 : (5*x + t) * 12/11

 (5*5 + 3) * 12/11

 28 * 12/11 = 336/11= 31511 min

therefore the hands will be 3 min apart at 31 5/11 min past 5.

Case 2 : (5*x - t) * 12/11

(5*5 -3 ) * 12/11

 22 *12/11 = 24 min 

 therefore the hands will be 3 min apart at 24 min past 5

Here the given number series  3, 10.5, 36.75, 128.625, ? follows a pattern that

3

3 x 3.5 = 10.5

10.5 x 3.5 = 36.75

36.75 x 3.5 = 128.625

128.625 x 3.5 = 450.187

Hence the next number in the given number series is 450.187.

The pattern followed is +3 , +6 , +12 , +24 , +48