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

To find:

(1) Total amount of A.

(2) Total amount of B.

Suppose A has Rs x and B has Rs y

According to the given conditions,

x + 100 = 2(y − 100)
x + 100 = 2y − 200
x − 2y = −300                  ....(1)
and

y + 10 = 6(x − 10)
y + 10 = 6x − 60
6x − y = 70                      ....(2)

Multiplying equation (2) by 2 we get

12x − 2y = 140               ....(3)

Subtracting (1) from (3),  we get

11x = 440
 x = 40

Substituting the value of x in equation (1), we get

40 − 2y = −300
−2y = −340
    y = 170

Hence $\mathrm{A}$ has $x=$ Rs 40 and $\mathrm{B}$ has $y=$ Rs 170