**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 times as rich as you." Tell me what is the amount of their respective capital?

**Solution:**

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 = 2*y *− 200*x *− 2*y* = −300 ....(1)

and*y* + 10 = 6(*x* − 10)*y* + 10 = 6*x* − 60

6*x* − *y* = 70 ....(2)

Multiplying equation (2) by 2 we get

12*x* − 2*y* = 140 ....(3)

Subtracting (1) from (3), we get

11*x* = 440* x* = 40

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

40 − 2*y* = −300

−2*y* = −340* y *= 170

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