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?
Let’s assume A has money = x
And B has money = y
Then according to the given conditions, we have
x – 100 = (y - 100) x (75/100)
x – 100 = (y - 100) x (3/4)
4x – 400 = 3y – 300
4x – 3y = 400 – 300
4x – 3y = 100 … (i)
Also,
x – 100 = (y + 100) (40/100)
x – 100 = (y + 100) (2/5)
5x – 500 = 2y + 200
5x – 2y = 200 + 500
5x – 2y = 700 … (ii)
Now, multiplying (i) by 2 and (ii) by 3, we have
8x – 6y = -1400
15x – 6y = 2100
(-)—(+)---(-)----
-7x = -3500
x = -3500/ -7
x = 500
On substituting the value of x in (i), we get
4(500) – 3y = -700
2000 – 3y = -700
3y = 2000 + 700
y = 2700/3
y = 900
Therefore, A has money Rs 500 and B has money Rs 900.
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