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.” Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II]

Ans.Let the money with the first person and second person be Rs x and Rs y respectively.

According to the question,
x + 100 = 2(y – 100)
x + 100 = 2y – 200
x – 2y = – 300… (1)
Also, 6(x – 10) = (y + 10)
6x – 60 = y + 10
6x – y = 70… (2)

Multiplying equation (2) by 2, we obtain:
12x – 2y = 140… (3)

Subtracting equation (3) from equation (1), we obtain:
11x = 140 + 300
=> 11x = 440
=> x = 40

Putting the value of x in equation (1), we obtain:
40 – 2y = –300
=> 40 + 300 = 2y
=> 2y = 340
=> y = 170

Thus, the two friends had Rs 40 and Rs 170 with them.