Question

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

Answer 1

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Answer 2

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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