Some boys are sitting in a row. P is 14th from the left end and Q is 7th from the right end. If there are exactly four boys between P and Q and Q is to the right of P, how many boys are there in the row?

Introduction / Context:
This ranking problem involves persons in a row where two positions are known from opposite ends and the number of persons between them is specified. Such questions test the ability to visualise a linear arrangement and apply consistent counting from both the left and the right ends of the row to determine the total number of persons.

Given Data / Assumptions:

• P is 14th from the left end of the row.
• Q is 7th from the right end of the row.
• There are exactly 4 boys between P and Q.
• We take the usual exam convention that Q is on the right side of P.
• The row is continuous with no gaps and all persons are counted once.

Concept / Approach:
When two persons in a row are at known positions from opposite ends and the number of persons between them is known, we can use a direct formula. Assuming that Q is to the right of P, the total number of boys in the row is given by: total boys = position of P from left + position of Q from right + number of persons between P and Q.
This formula effectively adds the segment from the left end to P, from P to Q including those in between, and from Q to the right end.

Step-by-Step Solution:
Step 1: Position of P from left = 14. Step 2: Position of Q from right = 7. Step 3: Number of boys between P and Q = 4. Step 4: Apply the formula: total boys = 14 + 7 + 4. Step 5: Compute 14 + 7 = 21. Step 6: Add the boys between: 21 + 4 = 25. Step 7: Therefore, there are 25 boys in the row.

Verification / Alternative check:
Assume there are 25 positions in the row. Q is 7th from the right, so Q is at position 25 - 7 + 1 = 19 from the left. P is at position 14 from the left. The number of boys between P (position 14) and Q (position 19) is 19 - 14 - 1 = 4, which matches the given condition. Thus a total of 25 boys is consistent with all the information provided.

Why Other Options Are Wrong:
Options 24, 26, and 22 do not satisfy all three conditions simultaneously. For these totals, either the distance between P and Q or the given ranks from the ends would not match the stated four boys between them.

Common Pitfalls:
A common difficulty is that, without a clear assumption on which side each person stands, two mathematical totals may appear possible. Standard exam convention assumes the second person described is to the right when their relative order is not explicitly stated. Another mistake is forgetting to include the boys between P and Q when adding the positions from left and right. Always carefully apply the appropriate formula and, if needed, cross check by constructing the row mentally.

Final Answer:
There are 25 boys in the row.