## 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 tim

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)

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

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2021-08-14T20:40:25+00:00
2021-08-14T20:40:25+00:00 2 Answers
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## Answers ( )

Solution :✪ Let the amount of capital with first person be x

✪ Now, let the amount of capital with second person be y

✞Accordingtothefirstcondition✒Second person gives Rs.100 to first person→ (x + 100) = 2(y – 100)

→ x + 100 = 2y – 200

→ x – 2y = – 100 – 200

→ (x – 2y) = – 300

–––(i)✞Accordingtothesecondcondition✒First person gives Rs.10 to second person→ 6(x – 10) = y + 10

→ 6x – 60 = y + 10

→ 6x – y = 60 + 10

→ (6x – y) = 70

––––(ii)✞Multiply(i)by1and(ii)by2✞Subtractboth the equations→ (x – 2y) – (12x – 2y) = -300 – 140

→ x – 2y – 12x + 2y = – 440

→ -11x = – 440

→ x = 440/11 = 40

✞Puttingthe value of x in equation(i)→ x – 2y = -300

→ 40 – 2y = – 300

→ – 2y = -300 – 40

→ – 2y = – 340

→ y = 340/2 = 170

Hence,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.