Question

One says give me a hundred friend i shall then become twice as rich as you.the other replies if you give me a ten i shall be six times as rich as you.tell me what is the amount of their respective capital

Answer 1

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.

Answer 2

$\red{\boxed{\huge Question}}$

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

$\huge\underline{\overline{\mid{\bold{ \red{To \: Find}}\mid}}} </p><p>$

What is the amount of their ( respective capital )

[from the Bijaganita of Bhaskara II ]

$\huge\underline{\overline{\mid{\bold{ \blue{Solution}}\mid}}} </p><p>$

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.