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

Solution: 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.