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)

x + 100 = 2(y − 100)

x + 100 = 2y − 200

x - 2y = -200 -100

x − 2y = −300……………….(1)

and

6(x − 10) = (y + 10)

6x − 60 = y + 10

6x - y = 10 +60

6x − y = 70…………………….(2)

By using elimination method

On Multiplying equ (2) by 2,

12x − 2y = 140……………….(3)

On Subtracting equation (1) from equation (3),

12x − 2y - (x − 2y ) = 140 - (-300)

12x - 2y - x + 2y = 140 + 300)

11x = 140 + 300

11x = 440

x = 440/11

x = 40

Put x = 40 in equation (1),

x − 2y = −300

40 − 2y = −300

40 + 300 = 2y

2y = 340

y = 340/2

y = 170

Hence, the amount of first friend capital is Rs.40 and the amount of second friend capital is Rs. 170.