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Pair Of Linear Equations In Two Variables

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)

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

Answer:

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 − ...

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