One says "Give me a 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." Find the amount of their capitals.

Let the capital of one is x and that of another is y .
According to the question.
x + 100 = 2(y - 100)
x + 100 = 2y - 200
or x - 2y = -300 ...(i)
Again, according to the question
y + 10 = 6(x - 10)
⇒ y + 10 = 6x - 10
⇒ 6x - y = 70 ..(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i) , we get
x - 2y = -300
12x - 2y = 140
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-11x = -440
∴ x = 40
On putting the value of x in Eq. (i) , we get
40 - 2y = -300
⇒ 2y = 340
∴ y = 170
So, their capital are ₹ 40 and ₹ 170.