In a row of people, Abhi’s position is 10th from the left and Appu’s position is 8th from the right. If Sam is sitting in the middle of Abhi and Appu and Sam’s position is 21st from the right, what is the total number of people in the row?
Question
In a row of people, Abhi’s position is 10th from the left and Appu’s position is 8th from the right. If Sam is sitting in the middle of Abhi and Appu and Sam’s position is 21st from the right, what is the total number of people in the row?
Solution
To solve this problem, we need to find the positions of Abhi, Appu, and Sam from a common point. We know Sam's position from the right (21st), so we'll use that as our reference point.
Step 1: Determine Abhi's position from the right. We know Sam is sitting in the middle of Abhi and Appu. Since Sam's position is 21st from the right and Appu's position is 8th from the right, there are 13 people between Sam and Appu. Therefore, Abhi's position must also be 13 people away from Sam, but on the other side. So, Abhi's position from the right is 21 (Sam's position) + 13 (distance to Abhi) = 34th from the right.
Step 2: Determine the total number of people in the row. We know Abhi's position from both the left (10th) and the right (34th). The total number of people in the row is therefore 10 (Abhi's position from the left) + 34 (Abhi's position from the right) - 1 (because Abhi is counted twice) = 43 people.
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