Question

15. 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 as rich as you." What is the amount of their capital?pls help
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Answer 1

Answer:

total capital: rs. 210

x= 40 y= 170

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that

First person is A and second person is B.

Let further assume that

Amount that person A have Rs x.

Amount that person B have Rs y.

According to first condition

A says to B, "Give me a hundred, friend! I shall then become twice as rich as you."

So,

A have Rs x + 100

B have Rs y - 100

Thus,

$\rm \: x + 100 = 2(y - 100)$

$\rm \: x + 100 = 2y - 200$

$\rm \: x = 2y - 200 - 100$

$\rm\implies \:\rm \: x = 2y - 300 - - - (1)$

According to second condition

B replies to A, "If you give me ten, I shall be six as rich as you."

So,

B have Rs y + 10

A have Rs x - 10

Thus,

$\rm \: y + 10 = 6(x - 10)$

$\rm \: y + 10 = 6x - 60$

$\rm \: y = 6x - 60 - 10$

$\rm \: y = 6x - 70$

On substituting the value of x, from equation (1), we get

$\rm \: y = 6(2y - 300) - 70$

$\rm \: y = 12y - 1800- 70$

$\rm \: y - 12y = - 1870$

$\rm \: - 11y = - 1870$

$\rm\implies \:y = 170$

On substituting the value of y in equation (1), we get

$\rm \: x = 2(170) - 300$

$\rm \: x = 340 - 300$

$\rm\implies \:x = 40$

Hence,

Amount that A have is Rs 40

Amount that B have is Rs 170