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.