Question

Question 2
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].

Answer 1

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.