Study Material for PSC exams Government Jobs:possible Math problem type; rate of income, rate of expense and rate of savings. An example

The ratio of incomes of two persons is 5:3 and that of their expenditures is 9:5.
Find the income of each person, if they save Rs.1300 and Rs. 900 respectively?
(FCI Assistant Grade- II)
Let "x" be the Total Income.
Let 'y' be the Total expenditure.

So total savings is X-Y
total savings also equal to 1300(savings of first person) + 900 (savings of second person) = 2200
hence Total savings, ie X-Y=2200



So income of first person is {5/(5+3)}*X
expenditure of first person is {(9/9+5)}*Y

Given that
(5/8)*X - (9/14)*Y = 1300 ie (Savings of first person)

5/8*(Y+2200) -(9/14)*Y =1300

Solving this we get,

Y=4200


Hence total expenditure of two person is Y= 4200

Now Total income of two persons is

saving + expenditure
(X-Y) + Y
! !
2200 + 4200 =6400

so Total income X =6400


Now,


5/8 * Total income = Income of first person

5/8 * X


5/8 * 6400

= 4000



Now income of second person


3/8 * 6400= 2400

or

(6400- 4000) = 2400


So income of first person is 4000
income of second person is 2400