Question

A and B play card on stake. A gains from B
1/4 of the latter's money. B gains from A
1/3 of A's original money. Each has now rs 400. How much money did each have before playing the game?
Well I tried this question a lot and have no clue how to do it

I made equation that after the game A has
X+1/4of Y-1/3ofX =400
And for B
Y+1/3of X-1/4of Y=400
But i think this may be wrong.
Please help me and provide me the equations and help a bit in that as well.

Answer 1

looks like they played two rounds of the game

A's original amount ---- x
B's original amount ---- y

after first round:
A has x+y/4
B has 3y/4

after 2nd round
A has x+y/4 - x/3
B has 3y/4 + x/3
....... You had that, good job, now just have to simplify the equations

x+y/4 - x/3 = 400
times 12, the LCD
12x + 3y - 4x = 4800
8x + 3y = 4800 **

3y/4 + x/3 = 400
times 12
9y + 4x = 4800
times 2
8x + 18y = 9600 ***

*** - **
15y = 4800
y = 320
into **
8x + 960 = 4800
x = 480

I will leave it up to you to verify this answer, (it works)

Answer 2

Thanks a lot