Trading Places

when carol becomes 15th from the left, she's 9th from the right. thats all you need to understand. the rest is addition(make sure you dont count carol twice and end up with 24 as your answer.)

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15(9) , 16(8) ,17(7) ,18(6) ,19(5) ,20(4), 21(3) , 22(2) ,23(1), = 23

Simple Logic .. 1. Carol is 10th from right and Jane is 9th from left 2 .When Carol is in Jane's position.....she is 15th from left and 9th from right So it is 15 + 9 but Then we count Carol twice . Hence 24 - 1 = 23

Let the total number of girls be n. Jane is 9th from right so she is (n-9+1) from left i.e, (n-8) now after interchange carol is 15th from left and it was Jane's position. So, now equating the relation n-8=15 gives n=23. So, total number of girls is 23.

Let Carol is 10 $^{th}$ from left, and Jane is 9 $^{th}$ from the right. If they interchange their seats, Carol becomes 15 $^{th}$ from the left. Which means, from the beginning Jane was 15 $^{th}$ from the left and 9 $^{th}$ from the right. Thus, the total girls in that row are 15+9-1=23

i guessed...

Carol(10th)interchanges seats(15th)and Jane still (9th from the right).the solution:15+9=24

firstly carol was 10th so 9 children were ahead then he was 15th so 14 were ahead and Jame was 9th so 8 were ahead then=14+8+carol

position (15+9)-1=23

from left carol is in 15th position and jane is in 9th position if they are interchanged carol is in 15 hence (15+9)-1=23 because 15 and 9 are same position....

I simply drew it out. _ _ _ _ _ _ _ _ _ Carol Jane _ _ _ _ _ _ _ _ Switch _ _ _ _ _ _ _ _ _ _ _ _ _ _ Carol(9)_ _ _ _ _ _ _ _ So counting all of the dashes + Carol's seat together, we get 23 since we know that after switching, Carol will have 8 seats to her right and 14 seats to her left concluding that 1+8+14 = 23!

15th from the left is 9 from right so total is 15 plus 8 which is 23

carol is 10th from left if he goes to 15th of left that means he is 9th from right to 15+9=23

Suppose whole number of them=x Carol was 10th from left and Jane is 9th from right There are =(10+9)=19 of them on left and right. In the middle there are (x-19) Then the equation =10+x-19=15-1

the carol is at 10th from left and Jane is at 9th from right. and they interchanged & now carol is at 15th that is 9th from right therefore no need to count the position twice .15 + 9 - 1 = 23

$n=\text{number of rows}$

$c=15$

$c=n-9+1=n-8$

$\therefore n-8=15$

$\therefore n=23$