Question

One says, “give me hundred, friend! I shall then become twice as rich as you” The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their respective capital?

Answer 1

Let the first person be A with x rupees, and the second person be B with y rupees.
When B gives A 100 rupees, then
x+100 = 2(y-100)
$\Rightarrow$ x-2​​​​​​​y =-300 ----- (i)

When A gives B 10 rupees,
y+10 = 6 (​​​​​​​x -10)

$\Rightarrow$ 6x-y =70

$\Rightarrow$ 12x-2y =140 -------(ii)

From (i) and (ii), x = 40 and y = 170

So A has 40 Rs and B has 170 Rs.