## 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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1 month 2021-08-14T20:40:25+00:00 2 Answers 0 views 0

1. ### Solution :

✪ Let the amount of capital with first person be x

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

According to the first condition

✒Second person gives Rs.100 to first person

• The amount of the 1st person = x + 100
• The amount of the 2nd person = y-100

→ (x + 100) = 2(y – 100)

→ x + 100 = 2y – 200

→ x – 2y = – 100 – 200

→ (x – 2y) = – 300 (i)

According to the second condition

✒First person gives Rs.10 to second person

• The amount of the 1st person = x – 10
• The amount of the 2nd person = y+10

→ 6(x – 10) = y + 10

→ 6x – 60 = y + 10

→ 6x – y = 60 + 10

→ (6x – y) = 70 (ii)

Multiply (i) by 1 and (ii) by 2

• x – 2y = -300
• 12x – 2y = 140

Subtract both the equations

→ (x – 2y) – (12x – 2y) = -300 – 140

→ x – 2y – 12x + 2y = – 440

→ -11x = – 440

→ x = 440/11 = 40

Putting the value of x in equation (i)

→ x – 2y = -300

→ 40 – 2y = – 300

→ – 2y = -300 – 40

→ – 2y = – 340

→ y = 340/2 = 170

Hence,

• The amount of capital with first person = x = Rs.40
• The amount of capital with second person = y = Rs.170
• One man says Give me a hundred freind
• and saying i will become twice rich than you
• the other man replies if you give me ten i shall give be six times rich as you

• What is the amount of their ( respective capital )
• (From the Bijaganita of Bhaskara II)

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.