**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.**