In a row of people, the position of Raju is 13th from the front side and 6th from the back side. How many people are standing in that row altogether?

Introduction / Context:
This is a standard rank and position problem in arithmetic reasoning. You are given the position of one person from the front and from the back in a single row, and you must determine the total number of people in that row. Questions like this are common in exams and are based on a simple but very important formula.

Given Data / Assumptions:

• Raju is 13th from the front.
• Raju is 6th from the back.
• All people stand in one straight row.
• Each person is counted only once, with no gaps or missing positions.

Concept / Approach:
When the position of the same person from the front and from the back is known, the total number of people in the row can be found using a simple relationship. That relationship is: total number of people = position from the front + position from the back - 1. The subtraction of 1 is necessary because the counted person is included in both the front and back counts.

Step-by-Step Solution:
Step 1: Note that Raju is 13th from the front, so there are 12 people in front of him.Step 2: Raju is 6th from the back, so there are 5 people behind him.Step 3: The total number of people is equal to number in front of Raju + Raju himself + number behind Raju.Step 4: That is 12 + 1 + 5 = 18.Step 5: Using the standard formula, total = 13 + 6 - 1 = 18, which matches the previous calculation.

Verification / Alternative check:
Imagine a row of 18 people numbered from 1 to 18 from the front. The 13th person from the front is at position 13. From the back, the positions are counted as 18, 17, 16, and so on. The person at position 13 from the front is at position 18 - 13 + 1 = 6 from the back, which exactly matches the given condition. This confirms that the total must be 18.

Why Other Options Are Wrong:
21, 20 and 19 all violate the formula total = front position + back position - 1, which gives 18.For 21, the person that is 13th from the front would be 21 - 13 + 1 = 9th from the back, not 6th.For 20, the person that is 13th from the front would be 20 - 13 + 1 = 8th from the back.For 19, the person would be 7th from the back.22 similarly gives a mismatch between front and back positions.

Common Pitfalls:
Students often forget to subtract 1 in the formula and mistakenly add the two positions directly, giving 19 instead of 18 in this case. Another mistake is to confuse the number of people in front or behind with the rank itself. Carefully visualising that the same person is counted in both directions prevents these errors. Writing the small formula and plugging in the values is the fastest and safest method.

Final Answer:
The total number of people standing in that row is 18.