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One says, “give me 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?

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Given:

One says, “give me 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.”

To find:

The amount of their respective capital.

Solution:

Let the capitals be ‘a’ and ‘b’.

Given, one says, “give me hundred, friend! I shall then become twice as rich as you”. Lets assume "b" gives hundred to "a". According to given condition a + 100 = 2(b – 100)

⇒ a + 100 = 2b - 200

⇒ a = 2b - 200 - 100

⇒ a = 2b – 300

⇒ a - 2b = - 300 ------ (1)

Now

The other replies, “If you give me ten, I shall be six times as rich as you.”

Which means "a" gives 10 to "b".

So,

b + 10 = 6(a – 10)

⇒ b + 10 = 6a – 60

⇒ b = 6a – 60 - 10

⇒ b = 6a – 70

⇒ 6a - b = 70 ----- (2)

Multiplying equation 1 by 6 and subtract from equation 2

⇒ 6a - b - 6 ( a - 2b ) = 70 - 6 (- 300)

⇒ 6a - b - 6 a + 12b = 70 + 1800

⇒ 11b = 1870

⇒ b = 170

substitute the value of b in equation 1 to get,

a - 2(170) = - 300

⇒ a - 340 = - 300

⇒ a = - 300 + 340

⇒ a = 40

The amount of their respective capital is Rs 40 and Rs 170.

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