# One says, “ Give me a hundred “ friend, I shall then become twice as rich as you”

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)

Let one friend has capital amount= x and other friend has capital amount =y
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.