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 B

Explanation

Let the amount of their respective capital's be Rs x and Rs y.
`therefore` According to the given condition,
x + 100 = 2 (y - 100)
implies x - 2y = - 300 …(1)
and 6(x - 10) = y + 10
implies 6x - y = 70 …(2)
On multiplying equation (2) by 2 and subtracting from equation (1) we get
x - 12 x = - 300 - 140
implies -11x = - 440 implies x = Rs. 40
On putting x - 40 in equation (1), we get
40 - 2y = - 300
implies 2y = 340 implies y = Rs. 170
Hence, the amount of their respective capitals are Rs. 40 and Rs. 170.