Difficulty: Easy
Correct Answer: 35
Explanation:
Introduction / Context:
This reasoning question involves understanding how positions from opposite ends of a row relate to the total number of people in the row. If a person has known positions from both the left and the right, you can use a simple formula to calculate the total number. This type of problem is frequently asked in verbal reasoning exams to check conceptual clarity rather than heavy calculation.
Given Data / Assumptions:
Concept / Approach:
There is a standard formula that links a person’s position from the left and right ends to the total number of people in a row. If a person is at position L from the left and at position R from the right, then the total number of people N is given by N = L + R - 1. Here, both L and R are 18. Substituting these values will directly give the total number of boys in the row.
Step-by-Step Solution:
Let L be Tarak’s position from the left and R be his position from the right.
Given that Tarak is 18th from one end and also 18th from the other, we have L = 18 and R = 18.
Use the relation N = L + R - 1 to find the total number of boys N.
Substitute L = 18 and R = 18: N = 18 + 18 - 1.
Compute: 18 + 18 = 36, and 36 - 1 = 35.
Therefore, there are 35 boys in the row.
Verification / Alternative check:
Imagine labeling the boys from left to right as positions 1 to 35. If Tarak is 18th from the left, he stands at position 18. Counting from the right, positions go from 35 down to 1, so position 18 from the right corresponds to 35 - 18 + 1 = 18 from the left, which matches. This confirms that a total of 35 boys is consistent with Tarak being 18th from both ends.
Why Other Options Are Wrong:
For 36 boys, a boy at position 18 from the left would be at position 36 - 18 + 1 = 19 from the right, not 18. Similarly, a total of 19 or 37 boys would place the central positions differently, and Tarak would not be 18th from both ends. Only a total of 35 boys allows a single boy to occupy symmetric positions 18 from each end.
Common Pitfalls:
A common error is to add the positions without subtracting 1, incorrectly using N = L + R, which would yield 36 instead of 35. Another pitfall is confusing the idea of the central position in an odd length row. Remember that when a person has the same position from both ends, the total number must be an odd number, and using the formula N = L + R - 1 is the safe method.
Final Answer:
The total number of boys in the row is 35.
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