Let the capitals be ‘a’ and ‘b’.

Given, 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.”

⇒ a + 100 = 2(b – 100)

⇒ a = 2b – 300 ------ (1)

Also, b + 50 = 5(a – 50)

⇒ b = 5a – 300 ----- (2)

Multiplying eq2 by 2 and adding to eq1

⇒ a – 2b + 2b – 10a = - 300 - 600

⇒ -9a = -900

⇒ a = 100

Thus, b = 500 – 300 = 200