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In a row, Amit is 10th from the front and Sumit is 25th from the back. If there are 5 people between them, how many people are in the row?
40
41
39
42
40
For ranking questions with people between two individuals, total people can either be a simple addition (non-overlapping case: Left + Right + Middle) or a minimum overlap case. Here, standard non-overlapping gives the maximum total: Position from front + Position from back + People between them.
For ranking questions with people between two individuals, total people can either be a simple addition (non-overlapping case: Left + Right + Middle) or a minimum overlap case. Here, standard non-overlapping gives the maximum total: Position from front + Position from back + People between them.
Analyze Positions from Both Ends
Amit is given as 10th from the front (left), meaning there are 9 people ahead of him before counting him. Sumit is 25th from the back (right), meaning there are 24 people behind him.
Account for People Between Them
There are 5 people sitting strictly between Amit and Sumit. Since the sum of their positions plus the people between them (10 + 25 + 5 = 40) is greater than any overlap condition, this is a straightforward non-overlapping linear arrangement.
Calculate Total Number of People
Total people in the row = Amit's rank from front (10) + Sumit's rank from back (25) + Number of people between them (5) = 10 + 25 + 5 = 40.
B: 41 is incorrect because it adds an extra person by miscalculating the positions. C: 39 is incorrect because it misses one person from the sum. D: 42 is incorrect as it overcounts by 2 persons.
A is correct because the total number of people in a linear row without overlapping is calculated by adding Amit's position from the front (10), Sumit's position from the back (25), and the number of people between them (5), resulting in 40.
Always check whether a ranking problem is a maximum case (non-overlapping) or a minimum case (overlapping) by comparing the sum of positions with the given intermediate count.
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