What should come next in the following number series?

9 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 7 6 5 4 3 2 1

There are 10 digits. Now, third digit from the right means (10-3+1 = ) 8th digit from the left.  But, from the question , third  and eighth digits are interchanged. Hence, the required digit is the third digit of the given number, ie 0.

Given Number:     4  2  1  5  7  9  3  6  8

Ascending order:  1  2  3  4  5  6  7  8  9

Hence the required pairs are  12, 49, 16

Given Number :  7 6 5 3 4 2 1 8 

New Number :    8 7  6 4 5 3 2 9

Ascending Order :  2 3 4 5 6 7 8 9 

Fifth digit in the above ascending order arrangement is '6' . Hence option(1) is the correct answer.

5th to the right of 12th digit from the right end means (12 - 5 = ) 7th digit from the right.ie 3.

We have to find out even number - even number - odd number sequence.

 8 5 8 6 7 6 8 9 3 2 7 5 3 4 2 2 3 5 5 2 2 8 1 1 9 3 1 7 5 1

 There are four such such even numbers: 6,8,2 and 8.

Three persons A, B, C can be arranged in a queue in six different ways, ie ABC, CBA, BAC, CAB, BCA, ACB. But since there are only 3 persons ahead of C, so C should be in front of the queue. Thus, there are only two possible arrangements, ie CBA and CAB.

We may consider the two cases as under:

Case I:  ←3C↔8B↔5A→21

Clearly, number of persons in the queue = (3+1+8+1+5+1+21=) 40

Case II:  ←3C A↔5B

Number of persons between A and C                  

= (8 - 6) = 2   

∵[C↔8B A→21B]

Clearly number of persons in the queue = (3+1+2+1+21) = 28

Now, 28 < 40. So, 28 is the minimum number of persons in the queue.                                                     

A > C  -----(i),   B > D  -----(ii),  E < B  --------(iii),  E > C  ---------(iv),  C > D  ---------(v)

from (i) and (v),   we get    A > C > D   ---------(I)

from (iii) and (iv), we get    B > E > C    --------(II)

From (I) and (II) , it is clear that 'D' is the thinnest.

W = 10th from the left

R = 4th from the right = (30 - 4 + 1= ) 27th from left

 No of boys between R and W = (27 - 10) - 1 = 16