points P and Q are on line segment AB on the same side of the midpoint of AB .Point P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4.If PQ =2 ,then the length of segment AB is ________

Answer 1

I drew a line AB, with A to the left of B
I marked P and Q on the left side of the midpoint.

"Point P divides AB in the ratio 2:3"
---> let AP = 2x and PB = 3x
then AB = 5x

"Q divides AB in the ratio 3:4"
--> let AQ = 3y and QB = 4y
then AB = 7y

clearly 7y = 5x or y = 5x/7 ***

Given:
PQ = 2
PQ = 3y - 2x

2 = 15/7x - 2x
14 = 15x - 14x
x = 14

then AB = 5x = 70

All the other segments can also be found