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

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− 200
− 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

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