The position-time graphs for two students A and B returning from the school to their homes are shown in figure.

(A) A lives closer to the school
(B) B lives closer to the school
(C) A takes lesser time to reach home
(D) A travels faster than B
(E) B travels faster than A
Choose the correct answer from the options given below

look at the graph slowly and interpret each thing correctly

horizontal axis → time
vertical axis → position (distance from school)

both students start from school (origin)

now key ideas
slope of line = speed
final height = how far their home is
final time coordinate = time taken

1. time taken

both lines end at the same time coordinate on x-axis
so both students reach home at the same time

so A does NOT take lesser time
(C) is wrong

2.who is faster

compare slopes

line B is steeper than A
steeper line → greater slope → higher speed

so B is faster
(E) is correct
(D) is wrong

3. who lives closer

compare final heights (end points on y-axis)

B’s endpoint is higher → B has travelled more distance
so B lives farther

A’s endpoint is lower → A lives closer

so (A) is correct
(B) is wrong

final answer: A and E