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Question

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].

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Solution

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 - 10) = (y + 10)

6x -60 = y +10

6x - y = 70 ---- (ii)

Multiplying equation (ii) by 2, we obtain

12x - 2y = 140 ------ (iii)

Subtracting equation (i) from equation (iii), we obtain

11x = 140 + 300

11x = 440

x = 40

Using this in equation (i), we obtain

40 - 2y = - 300

40 + 300 = 2y

2y = 340

y = 170

Therefore, those friends had Rs 40 and Rs 170 with them respectively.

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 - 10) = (y + 10)

6x -60 = y +10

6x - y = 70 ---- (ii)

Multiplying equation (ii) by 2, we obtain

12x - 2y = 140 ------ (iii)

Subtracting equation (i) from equation (iii), we obtain

11x = 140 + 300

11x = 440

x = 40

Using this in equation (i), we obtain

40 - 2y = - 300

40 + 300 = 2y

2y = 340

y = 170

Therefore, those friends had Rs 40 and Rs 170 with them respectively.

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