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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) Expert Answer
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.
Answered by Arun | 07 Jun, 2018, 10:47: AM
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