please solve this problem by using simultaneous linear equation(can be by elimination method)
please give me the full solution with the equation formed.
the problem is:A and B have some money with them.A said to B ,"if u give me 100rupees my money will become 75% of the money left with u". B said to A,"instead if u give me 100rupees your money will become 40% of my money.How much money did A & B have originally?  

Asked by naganshul258 | 6th Jun, 2017, 12:56: PM

Expert Answer:

begin mathsize 16px style Let space the space money space with space straight A thin space be space Rs. space straight x space and space with space straight B space be space Rs. space straight y.
Then comma space we space have
straight x plus 100 equals 75 percent sign space of space left parenthesis straight y minus 100 right parenthesis
rightwards double arrow straight x plus 100 equals 75 over 100 cross times straight y minus 75
rightwards double arrow straight x plus 100 equals 3 over 4 cross times straight y minus 75
rightwards double arrow straight x minus fraction numerator 3 straight y over denominator 4 end fraction equals negative 75 minus 100
rightwards double arrow fraction numerator 4 straight x minus 3 straight y over denominator 4 end fraction equals negative 175
rightwards double arrow 4 straight x minus 3 straight y equals negative 700 space space space space space space space space space space.... left parenthesis straight i right parenthesis
Also comma
straight x minus 100 equals 40 percent sign space of space left parenthesis straight y plus 100 right parenthesis
rightwards double arrow straight x minus 100 equals 40 over 100 straight y plus 40
rightwards double arrow straight x minus 100 equals 2 over 5 straight y plus 40
rightwards double arrow straight x minus 2 over 5 straight y equals 40 plus 100
rightwards double arrow fraction numerator 5 straight x minus 2 straight y over denominator 5 end fraction equals 140
rightwards double arrow 5 straight x minus 2 straight y equals 700 space space space space space space space space space space.... left parenthesis ii right parenthesis
Multiplying space left parenthesis straight i right parenthesis space by space 2 space and space left parenthesis ii right parenthesis space straight b space 3 comma space we space get
8 straight x minus 6 straight y equals negative 1400 space space space space space space space space space space.... left parenthesis iii right parenthesis
15 straight x minus 6 straight y equals 2100 space space space space space space space space space space space space.... left parenthesis iv right parenthesis
Subtracting space left parenthesis iii right parenthesis space from space left parenthesis iv right parenthesis comma space we space get
7 straight x equals 3500
rightwards double arrow straight x equals 500
Substituing space straight x equals 500 space in space left parenthesis ii right parenthesis comma space we space get
5 cross times 500 minus 2 straight y equals 700
rightwards double arrow 2500 minus 2 straight y equals 700
rightwards double arrow 2 straight y equals 1800
rightwards double arrow straight y equals 900
Thus comma space originally space straight A space has space Rs. space 500 space and space straight B space has space Rs. space 900. end style

Answered by Rashmi Khot | 6th Jun, 2017, 03:14: PM