Question

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? (a) 60, 180 (b) 20, 190 (c) 40, 170 (d) 100, 200​

Answer 1

Answer:

Let us assume that First man is A and second Man is B.

Next assumption be man A have Rs x

and second man have Rs. y

According to first given condition,

$\red{x + 100 = 2(y - 100)}$

$\red{x + 100 = 2y - 200}$

$\red{x = 2y - 200 - 100}$

$\red{ \implies \: x = 2y - 300} \: ...eq(1)$

According to second given condition.

$\red{y + 10 = 6(x - 10)}$

$\red{y + 10 = 6x - 60}$

$\red{y = 6x - 60 - 10}$

$\red{y = 6x - 70}$

Substituting value of x from eq(1),

$\red{y = 6(2y - 300) - 70}$

$\red{y = 12y - 1800 - 70}$

$\red{y - 12y = - 1870}$

$\red{ - 11x = - 1870}$

$\red{ \implies \: y = 170}$

Substitute value of y in eq ( 1 ) ,

$\red{x = 2(170) - 300}$

$\red{x = 340 - 300}$

$\red{ \therefore \: x = 40}$

Therefore,

First man have Rs 40.And second man have Rs. 170