Question

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $4$ times as much money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?

Answer 1

Answer:

y:x = 31:9

Step-by-step explanation:

Let amount with Bob = x$

Let amount with Alice = y$

Case-I: Bob gives n$ to Alice

Then,

Amount left with Bob = (x-n)$

Amount with Alice = (y+n)$

Given, y+n = 4(x-n) -eqn1

Case-II: Alice gives n$ to Bob

Then,

Amount with Bob = (x+n)$

Amount left with Alice = (y-n)$

Given, y-n = 3(x+n) -eqn2

By solving eqn1 and eqn2 you get,

x = 9n$ , y = 31n$

Ratio = y:x = 31:9