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.