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 (respectively) capital ?

Solution :

Let two friends named as P and Q. Let P has Rs x and Q has Rs y.

According to Question,

x + 100 = 2(y – 100)

\(\implies\)  x – 2y + 300 = 0           ………(1)

y + 10 = 6(x – 10)

\(\implies\)  6x – y – 70 = 0             ………(2)

Multiply equation (2) by 2 and subtract from equation (1), we get

-11x = -440  \(\implies\)  x = 40

Put the value of x = 40 in equation (1), we get

40 – 3y + 300 = 0    \(\implies\)  y = 70.