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In a row of students, Rohan is 15th from the left and Priya is 22nd from the right. If they interchange their positions, Rohan becomes 20th from the left. How many students are there in the row?
40
41
42
39
41
Quick Trick: Total students = New position of one person from one side + Old position of the other person from the opposite side - 1.
Total students = New position of one person from one side + Old position of the other person from the opposite side - 1.
Analyze initial positions
Rohan is 15th from the left and Priya is 22nd from the right.
Apply interchange logic
After interchanging, Rohan occupies Priya's old spot, meaning Rohan is now 20th from the left and 22nd from the right.
Calculate total students
Total = (Rohan's new left position) + (Rohan's right position) - 1. So, 20 + 22 - 1 = 41.
A: 40 is incorrect as it results from miscalculating the overlap (20+22-2), C: 42 is incorrect as it fails to subtract the shared position, D: 39 is incorrect as it uses erroneous additions (15+22+2).
B is correct because the total number of students is determined by adding the new position of Rohan from the left (20) to the position of Priya from the right (22) and subtracting 1 to account for the double-counting of the same position.
In interchange problems, always identify the specific person whose position is given from both sides after the swap; this is the key to calculating the total row size.