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 ) ]​

Answer 1

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• 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

$\huge\underline{\overline{\mid{\bold{ \red{To \: Find}}\mid}}}$

• What is the amount of their ( respective capital )

• (From the Bijaganita of Bhaskara II)

$\huge\underline{\overline{\mid{\bold{ \blue{Solution}}\mid}}}$

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

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