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?

Let the initial amount with them beRs. xandRs. yrespectively.Then according to the question:x+100=2(y−1;00)x+100=2y−2;00x−2;y=−300…(1)And,6(x−1;0)=(y+10)6x−6;0=y+106x−y=70…(2)Multiplying equation(2)by 2, we get:12x−2;y=140…(3)Subtracting equation(1)from equation(3), we get:11x=140+30011x=440x=40Substitute the vale ofxin equation(1), we get:40−2;y=−30040+300=2y2y=340y=3402=170∴The friends hadRs. 40andRs. 170with them respectively.