Question

In a row of 40 children, A is 13th from the left end and B is ninth from the right end. How many children are there between A and C if C is fourth to the left of B.

• A. \( 13 \)
• B. \( 14 \)
• C. \( 15 \)
• D. \( 16 \)

Hint:

\textbf{Linear Arrangement and Position Problems.} In problems involving the arrangement of items in a row, it's often helpful to determine the position of each item from a single reference point (usually the left end). Use the given information to find these positions and then calculate the number of items between them by taking the difference of their positions and subtracting (A)

Answer 1

The Correct Option is B

Total number of children in the row = 40. Position of A from the left end = 13th. Position of B from the right end = 9th. To find the position of B from the left end, we use the formula: Position from left = Total number of children - Position from right + 1 Position of B from the left end \( = 40 - 9 + 1 = 31 + 1 = 32 \)nd. C is fourth to the left of B. Since we are considering the positions from the left end, moving to the left means decreasing the position number. Position of C from the left end \( = \text{Position of B from the left end} - 4 \) Position of C from the left end \( = 32 - 4 = 28 \)th. Now we have the positions of A and C from the left end: Position of A from the left = 13th. Position of C from the left = 28th. Since the position of A is less than the position of C, A is to the left of C. The number of children between A and C can be found by subtracting their positions and then subtracting 1: Number of children between A and C \( = (\text{Position of C from left} - \text{Position of A from left}) - 1 \) Number of children between A and C \( = (28 - 13) - 1 \) Number of children between A and C \( = 15 - 1 \) Number of children between A and C \( = 14 \) Therefore, there are 14 children between A and C.