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  • 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]

Q2. 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)].

Answers (1)

best_answer

Let the amount of money the first person and the second person have is x and y, respectively

Now, according to the question,.

x + 100 = 2(y - 100)

\Rightarrow x - 2y =-300...........(1)

Also

y + 10 = 6(x - 10)

\Rightarrow y - 6x =-70..........(2)

Multiplying (2) by 2, we get,

2y - 12x =-140..........(3)

Now, adding (1) and (3), we get

-11x=-140-300

\Rightarrow 11x=440

\Rightarrow x=40

Putting this value in (1)

40-2y=-300

\Rightarrow 2y=340

\Rightarrow y=170

Thus, two friends had 40 and 170 rupees, respectively.

 

Posted by

Pankaj Sanodiya

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