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.
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)
Thanks a lot
To solve this problem, we can set up a system of equations based on the given information.
Let's assume that A initially had X amount of money, and B initially had Y amount of money.
According to the given information, A gains 1/4 of B's money, so A gains (1/4)Y. Therefore, A now has X + (1/4)Y.
Similarly, B gains 1/3 of A's original money, so B gains (1/3)X. Therefore, B now has Y + (1/3)X.
We also know that after the game, each of them has 400 rupees. So we can set up the following system of equations:
Equation 1: X + (1/4)Y = 400
Equation 2: Y + (1/3)X = 400
Now, we need to solve this system of equations to find the values of X and Y.
One way to solve this system is by using substitution. We can solve Equation 1 for X and substitute it into Equation 2.
From Equation 1, we have X = 400 - (1/4)Y.
Substituting this value of X into Equation 2, we get:
Y + (1/3)(400 - (1/4)Y) = 400
Now, we can solve this equation for Y.
Simplifying the equation:
Y + (1/3)(400) - (1/3)(1/4)Y = 400
Y + 400/3 - Y/12 = 400
(12/12)Y + (1600/3)/12 - (1/12)Y = 400
(11/12)Y + (1600/36) - (1/12)Y = 400
(10/12)Y + (1600/36) = 400
(10/12)Y = 400 - (1600/36)
(10/12)Y = 300
Multiplying both sides of the equation by 12/10 to solve for Y:
Y = (300) * (12/10)
Y = 360
Now that we have the value of Y, we can substitute it back into Equation 1 to find X:
X + (1/4)(360) = 400
X + 90 = 400
X = 400 - 90
X = 310
So, the initial amount of money A had (X) was 310 rupees, and the initial amount of money B had (Y) was 360 rupees.