Question

A and B have some money with them. A said to B, 'if you give me 100, my money win become 75% of the money left with you. "B said to A" instead if you give me 100, your money will become 40% of my money. How much money did A and B have originally?

Answer 1

let money of A is x rs

money of B is y rs

75 % (y - 100) = x +100

75 / 100 (y - 100) = x +100

3/ 4 (y - 100) = x +100


3y - 300 = 4x + 400

3y - 4x = 700 ------ ( 1 )


now


x -100 = 40 % ( y+100 )

x -100 = 2/5 ( y+100 )

5x - 500 = 2y + 200


-2y + 5x = 700 ------ ( 2 )

multiplying eq 1 by 2 and eq 2 by 3

6y - 8x = 1400 ------ ( 3 )

-6y + 15x = 2100 ------ ( 4 )

adding 3 and 4 we get


7x = 3500

x = 500 rs

putting this value in eq 1 we get

y = 900 rs

Answer 2

Let A has money = x Rs and B has money = y Rs
Then (x+100) = 3/4(y-100) and (x-100) = 2/5 (y+100)
so 4x + 400 = 3y - 300 and 5x -500 = 2y + 200
4x - 3y = - 300 - 400 and 5x - 2y = 200 + 500
4x - 3y = - 700 and 5x - 2y = 700
(x 5) 20 x - 15 y = - 3500 ( i ) and (x 4) 20 x - 8 y = 2800 ( ii )
By subtracting ( i ) from ( ii )
20 x - 8 y - 20 x + 15 y = 2800 + 3500
7 y = 6300
y = 900
By putting value of y in eq ( ii )
20 x - 8 y = 2800
20 x - 8x900 = 2800
20 x - 7200 = 2800
20 x = 2800 + 7200
20 x = 10000
x = 500
Now x = 500 and y = 900
Thus A has money = 500 Rs and B has money = 900 Rs Answer