In a row of 50 books, Book A is 15th from left and Book B is 20th from right. How many books lie between them?
- (a)17
- (b)15
- (c)12
- (d)10
Answer
Why
Correct — B.
Rule: count both books from the same end, subtract, then take away 1.
B from the left = 50 − 20 + 1 = 31st
A from the left = 15th
Books between = 31 − 15 − 1 = 15 → option (b).
Check: A's 15 and B's 20 do not overlap (15 + 20 = 35), so 50 − 35 = 15 lie between.
Why the others are wrong
- (a)17 — 17 is 31 − 15 + 1, the count from A to B including both books. The question asks for the books between them, which leaves out A and B.
- (c)12 — 12 would put B 28th from the left, which is 23rd from the right, not 20th. With B 31st, positions 16 to 30 lie between: 15 books.
- (d)10 — 10 would need B to stand 26th from the left, which is 25th from the right. B is 20th from the right, so 31st from the left.
Concept
A row question gives two ranks from opposite ends. Convert one of them so both count from the same end: rank from the left = total − rank from the right + 1.
The books strictly between are then the difference minus 1. When the two stretches do not overlap, the same count comes out as total − (left rank + right rank): here 50 − 35 = 15.
Check the order first. B is 31st from the left and A is 15th, so B stands to the right of A and the two stretches do not overlap. If they overlapped, the count would work differently.
Key facts
- Rank from the left = total − rank from the right + 1.
- Number strictly between ranks p and q counted from the same end = q − p − 1.
- When the two ranks do not overlap, the number between = total − (left rank + right rank).
Study next
Common traps
- Counting from A to B inclusive and choosing 17
- Forgetting the + 1 when converting B's rank to a rank from the left
15 Sep 2025, 16:00, Reasoning Q.14 sets a row of 60: Meena 25th from the left, Rupa 20th from the right. Rupa is 41st from the left, and 41 − 25 − 1 = 15 is keyed.
14 Sep 2025, 09:00, Reasoning Q.14 does it with 40 students, keyed 10.
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