200 people are sitting in a row. Asha is in the 20th place from the left and Anna is in the 31st position from the right. How many people are sitting between them?
Finding People Between Two Individuals in a Row
This problem involves calculating the number of people sitting between two individuals, Asha and Anna, in a linear arrangement of 200 people. We are given their positions from opposite ends of the row.
Understanding Positions in a Row
When someone is in the Nth position from the left, it means there are \(N-1\) people to their left. Similarly, if someone is in the Mth position from the right, there are \(M-1\) people to their right.
- Total number of people in the row = 200
- Asha's position from the left = 20th
- Anna's position from the right = 31st
Calculating People Based on Positions
Asha is at the 20th position from the left. This means there are 19 people sitting to her left.
\[ \text{Number of people to Asha's left} = \text{Asha's position} - 1 = 20 - 1 = 19 \]Anna is at the 31st position from the right. This means there are 30 people sitting to her right.
\[ \text{Number of people to Anna's right} = \text{Anna's position} - 1 = 31 - 1 = 30 \]Determining if Positions Overlap
To find the number of people between Asha and Anna, we first need to consider if their positions overlap or not. In a row of 200 people:
- Asha is 20th from the left.
- Anna is 31st from the right. The position of Anna from the left end can be calculated as: \[ \text{Anna's position from left} = \text{Total people} - \text{Anna's position from right} + 1 \] \[ \text{Anna's position from left} = 200 - 31 + 1 = 170 \]
Since Asha's position (20th from left) is less than Anna's position (170th from left), Asha is to the left of Anna. Their positions do not overlap in a way that would cause confusion in counting people between them using the simple subtraction method.
Finding the Number of People Between Asha and Anna
The total number of people in the row includes the people to the left of Asha, Asha herself, the people between Asha and Anna, Anna herself, and the people to the right of Anna.
\[ \text{Total people} = (\text{People to left of Asha}) + \text{Asha} + (\text{People between Asha and Anna}) + \text{Anna} + (\text{People to right of Anna}) \]We know:
- People to left of Asha = 19
- Asha = 1 person
- Anna = 1 person
- People to right of Anna = 30
Let \(x\) be the number of people between Asha and Anna. The equation becomes:
\[ 200 = 19 + 1 + x + 1 + 30 \] \[ 200 = 51 + x \]Now, solve for \(x\):
\[ x = 200 - 51 \] \[ x = 149 \]So, there are 149 people sitting between Asha and Anna.
Alternatively, we can think of the people not between Asha and Anna. These are the people up to Asha from the left (inclusive) and the people up to Anna from the right (inclusive). Since there is no overlap, we can simply sum these counts and subtract from the total.
- Number of people up to Asha from the left = 20
- Number of people up to Anna from the right = 31
- Total people accounted for from the ends = \(20 + 31 = 51\)
These 51 people are the set of people starting from the left up to Asha, and the set of people starting from the right up to Anna. The people between Asha and Anna are everyone else in the row.
\[ \text{People between} = \text{Total people} - (\text{People up to Asha from left}) - (\text{People up to Anna from right}) + 2 \]This formula is incorrect for this scenario. Let's stick to the first method or refine the second one.
Refined Second Method:
- Number of people NOT between Asha and Anna = (People to the left of Asha) + Asha + (People to the right of Anna) + Anna
- Number of people NOT between Asha and Anna = 19 + 1 + 30 + 1 = 51
- Number of people between Asha and Anna = Total people - (Number of people NOT between Asha and Anna)
- Number of people between Asha and Anna = \(200 - 51 = 149\)
Both methods yield the same result, confirming that 149 people are sitting between them.
Conclusion
Based on the positions given, the number of people sitting between Asha and Anna is 149.
The final answer is 149.
Important Questions from Rank Based
In a row of forty children, R is eleventh from the right end and there are fifteen children between R and M. What is M’s position from the left end of the row?
Keerthi ranked 17 th from the top in a class of thirty-one students. What is his rank from the bottom?
Shahid and Purnima are standing in queue for a railway ticket. Shahid is the 7 th from the counter and the 27 th from the end. Purnima is the 12th from the end. How many people are ahead of her?
Price of five cars A, L, J, M and T are compared. Price of A is the least. No two cars have the same price. Price of J is less than T. L and M. Price of neither T nor L is the highest. Price of T is less than L. Price of how many cars is more than the price of T?
In a queue, A stands 14th from the front and B 17th from the last. C is exactly at the middle of the queue with 16 persons between him and A. How many persons are between B and C?
