Question

divide 34 into 2 parts in such a way that four seventh of one part is equal to twofifth of the other

Answer 1

let one part be x and other be 34x. now 4\7*x=4x\7. and 2\5*34-x=68-2x\5. Now these two parts are equal so. 4x\7=68*2x\5 by cross multiplication we get 20x = 476 -14x. 20x+14x=476. 34x=476.
x=14
So other part is 34 - 14 = 20.
So parts are 14 and 20