How much did Akansha and Jyotsna have at the beginning of their exchange?

Question

Akansha gave Jyotsna as many dollars as Jyotsna started out with.

Jyotsna then gave Akansha back as much as Akansha had left.

Akansha then gave Jyotsna as back as many dollars as Jyotsna had left;

which left Akansha broke and gave Jyotsna a total of $80.00.

How much did Akansha and Jyotsna have at the beginning of their exchange?

Answer 1

Akanksha 50 and Jyotsna 30
let us start with Akanksha x and Jyotsna y dollars
Akanksha Jyotsna
After first transfer x-y y+y
After second transfer x-y+x-y =2x-2y y+y-(x-y) =3y-x
After third transfer 2x-2y-(3y-x)=3x-5y 3y-x+(3y-x)=6y-2x..........(1)
Akanksha becomes broke means 3x-5y=0 or x=(5/3)y substitute in (1) Jyotsna=6y-(10/3)y=(8/3)y=80 dollars or y=30 and x=50
(HAVE CHECKED WITH THE LOGIC, ANSWER IS CORRECT)