Question

One says," give me a 100, friend! I shall then become twice as rich as you". The other replies, "If you give me 10, I shall be six times as rich as you." Tell me what is the amount of their capital?

Answer 1

Let first person be A and second person be B
Let A have x and B have y initially,
If B gives A 100, then A becomes twice as rich as B
So x+100 = 2(y-100) (1)
If A gives B 10 then B becomes 6 times as rich as A
So y+10 = 6(x-10) (2)

From (1) x+100 = 2y-200
=> x-2y= -300 (3)
From (2) y+10=6x-60
=> 6x-y = 70 (4)
Multiply (3) by -6 and add to (4)
-6x+12y=1800
6x-y = 70
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11y =1870
y = 170
substitute in (3) x-2(170) = -300
x-340= -300
x= 40
Answer" 40 and 170