The ratio of the incomes of P and Q is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves 1600, then the income of P is

The ratio of the incomes of P and Q is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves 1600, then the income of P is=?

Solution :

1.       Let income of P and Q are PI and QI,then PI/QI=5/4,THEN QI=4/5.PI

2.       Let expenditure of P and Q are PE and QE,then PE/QE=3/2 ,THEN PE=3/2.QE

3.       Saving =Income -expenditure

4.       Saving of P is PI-PE=1600 AND QI-QE=1600, then QE=QI-1600

5.       We need income of P=PI

   From above (4) we know PI-PE=1600, Then replacing PE value from above (2), PI-3/2XQE=1600, then replacing QE from above (4), PI-3/2(QI-1600) =1600, then replacing QI from above (1), PI-3/2(4PI/5-1600) =1600, then PI-12PI/10+2400=1600, then -2PI/10=-800, then 2PI=8000, then PI=4000(ANSWER).