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”. Tell me what is the amount of their respective capital?
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 do:
We have to find the amount of their respective capital.
Solution: Let the capital with the first friend and the capital with the second friend be $x$ and $y$ respectively.
If the first friend gets 100 from the second friend then the money with first friend is $x+100$ and the money with the second friend is $y-100$.
If the second friend gets 10 from the first friend then the money with the first friend is $x-10$ and the money with the second friend is $y+10$.
According to the question,
$x + 100 = 2(y-100)$.....(i)
$y + 10 = 6(x-10)$
$y+10=6x-60$
$y=6x-60-10$
$y=6x-70$.....(ii)
Substituting $y=6x-70$ in equation (i), we get,
$x+100=2(6x-70-100)$
$x+100=12x-340$
$12x-x=100+340$
$11x=440$
$x=\frac{440}{11}$
$x=40$
This implies,
$y=6(40)-70$
$y=240-70$
$y=170$
The capital with the first friend is Rs. 40 and the capital with the second friend is Rs. 170.
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