In a row of forty children, R is eleventh from the right end and there are fifteen children between R and M. What is M’s position from the left end of the row?
Fourteenth
Determining Children Row Position
This problem involves finding the position of a child (M) in a row based on the position of another child (R) and the number of children between them. We need to use logical deduction and basic arithmetic.
Calculating R’s Position from the Left
First, let’s find out where R is standing from the left end of the row.
- Total number of children in the row = 40.
- R’s position from the right end = 11th.
To find R’s position from the left end, we use the formula:
R’s position from left = (Total children) - (R’s position from right) + 1
Substituting the values:
R’s position from left = 40 - 11 + 1
R’s position from left = 29 + 1
R’s position from left = 30
So, R is the 30th child from the left end.
Finding M’s Position from the Left
We are given that there are 15 children between R and M.
R is at the 30th position from the left.
There are two possibilities for M’s position relative to R:
- M is to the left of R.
- M is to the right of R.
Possibility 1: M is to the Left of R
If M is to the left of R, we count backwards from R’s position.
M’s position from left = (R’s position from left) - (Number of children between R and M) - 1
M’s position from left = 30 - 15 - 1
M’s position from left = 15 - 1
M’s position from left = 14
So, M could be the 14th child from the left.
Possibility 2: M is to the Right of R
If M is to the right of R, we count forwards from R’s position.
M’s position from left = (R’s position from left) + (Number of children between R and M) + 1
M’s position from left = 30 + 15 + 1
M’s position from left = 45 + 1
M’s position from left = 46
This position (46th) is impossible because there are only 40 children in the row.
Conclusion on M’s Position
Since the 46th position is not valid, the only possible position for M from the left end is the 14th position.
| Detail | Value |
|---|---|
| Total Children | 40 |
| R’s Position (Right) | 11 |
| Children between R & M | 15 |
| R’s Position (Left) | 30 |
| M’s Possible Position (Left) | 14 or 46 |
| Valid M’s Position (Left) | 14 |
Therefore, M’s position from the left end of the row is 14th.
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