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)].
Let Sangam have Rs A with him and Reuben have Rs B with him.
Using the information that is given we get,
A + 100 = 2(B – 100)
⇒ A + 100 = 2B – 200
Or A – 2B = -300 ............(1)
And
6(A – 10) = ( B + 10 )
Or 6A – 60 = B + 10
Or 6A – B = 70 ..........(2)
When equation (2) is multiplied by 2 we get,
12A – 2B = 140 ..........(3)
When equation (1) is subtracted from equation (3) we get,
11A = 140 + 300
11A = 440
⇒ A = 440/11 = 40
Using A = 40 in equation (1) we get,
40 – 2B = -300
40 + 300 = 2B
2B = 340
B = 170
Therefore, Sangam had Rs 40 and Reuben had Rs 170 with them.