In this type of questions, generally the ranks of a person from the top and from the bottom are mentioned and the total number of persons is asked. However, sometimes, this question is put in the form of a puzzle of interchanging seats by two persons.
Practice Questions:
Question 1
Sam ranked ninth from the top and thirty-eighth from the bottom in a class. How many students are there in the class?
Number of students in the class = 8 + 1 + 37 = 46.
Question 2
In a row of boys, Jeevan is seventh from the start and eleventh from the end. In another row of boys, Vikas is tenth from the start and twelfth from the end. How many boys are there in both the rows together?
Boys in Jeevan row + Boys in Vikas row = Total boys
(6 + 1 + 10) + (9 + 1 + 11) = 17 + 21 = 38.
Question 3
A class of boys stands in a single line. One boy is nineteenth in order from both the ends. How many boys are there in the class?
Number of boys in the class = 18 + 1 + 18 = 37.
Question 4
In a class of 60, where girls are twice that of boys, Kamal ranked 17th from the top. If there are 9 girls ahead of Kamal, how many boys are after him in rank?
Let the number of boys be x. Then the number of girls is 2x.
x + 2x = 60; 3x = 60; x = 20
So, number of Boys = 20 and number of Girls = 40
Number of students behind Kamal in rank = 60 - 17 = 43
Number of girls ahead of Kamal in rank = 9
Number of girls behind Kamal in rank = 40 - 9 = 31
Thus, number of boys behind Kamal in rank = 43 - 31 = 12.
Question 5
Ajay ranked 16th from the top and 29th from the bottom among those who passed an examination. Six boys did not participate in the competition and five failed in it. How many boys were there in the class?
Number of boys who passed = 15 + 1 + 28 = 44
Total number of boys = 44 + 6 + 5 = 55.
Time to Think:
If Atul finds that he is 12th from the right in a line of boys and 4th from the left, how many boys should be added to the line such that there are 28 boys in the line?
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