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)
[Hint: x + 100 = 2 (y - 100), y + 10 = 6(x - 10)]

Question

Philoid · Accepted Answer

Let those friends were having Rs x and y with them. Using the information given in the question,

we obtain x + 100 = 2(y - 100)

x + 100 = 2y - 200 x - 2y = -300 (i)

And, 6(x - 10) = (y + 10) 6x - 60 = y + 10

6x - y = 70 (ii)

Multiplying equation (ii) by 2, we obtain 12x - 2y = 140 (iii)

Subtracting equation (i) from equation (iii),

we obtain 11x = 140 + 300

11x = 440 x = 40

Using this in equation (i), we obtain 40 - 2y = -300

40 + 300 = 2y

2y = 340 y = 170

Therefore, those friends had Rs 40 and Rs 170 with them respectively.