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.
