Answer :

Given: 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".

To find: the amount of their respective capital.

Solution:

Let the capital of two friends be ‘a’and ‘b’ respectively.

Given, one says, “Give me a hundred, friend! I shall then become twice as rich as you.

It means if one is giving Rs. 100 other is losing the Rs. 100.

Since a is gaining 100 and b is losing 100.

⇒ a + 100 = 2(b – 100)

⇒ a + 100 = 2b – 200

⇒ a - 2b = -200 - 100

⇒ a - 2b = -300        ...... (1)

In another condition 2nd friend replies, “Give me a ten, I shall be six times as rich as you".

It means if one person is gaining 10 other person is losing 10.

Here b is gaining Rs 10 and a is losing Rs 10.

⇒ b + 10 = 6(a – 10)

⇒ b + 10 = 6a – 60

⇒ 6a - b = -60-10

⇒ 6a - b = -70        ...... (2)

Now solve equations (1) and (2) to get the amount a and b.

Multiply eq. (1) with 6 and subtract we. (2) from it.

⇒6(a - 2b )-(6a - b) = 6 (-300) -70

⇒6a - 12b-6a+b = -1800 -70

⇒ -11b= -1870

⇒ b = 170

put the value of b in the eq.(1) to get value of a,

⇒a - 2(170) = -300

⇒a - 340 = -300 

⇒ a = -300 + 340

⇒ a= 40

Hence the amount of capital of two friends is Rs 40 and Rs 170. 

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