Question

the ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3 if each of them manages to save 2000rs per month find their monthly income

Answer 1

Let the income of both person be 9a and 7a

And expenditures of both be 4b and 3b respectively

Savings = 2000

=> 9a - 4b = 2000

=> 27a - 12b = 6000 -------(1)

And,

7a - 3b = 2000

=> 28a - 12b = 8000 -------(2)

On subtracting equation 1 from 2, we get

a = 2000


Monthly incomes are 18,000 and 14,000

Answer 2

Let the common ratio  be x.

Given that the ratio of incomes of two persons is 9:7.

= > Income of 1st person = 9x.

= > Income of 2nd person = 7x.


Given that ratio of their expenditures is 4:3.

= > Expenditure of 1st person = 4x.

= > Expenditure os 2nd person = 3x.


Given that they manage to save 2000rs per month.

= > 9x - 4y = 2000   -------- (1)   ------- 1st person income and expentiure

= > 7x - 3y = 2000   ------- (2)   ------- 2nd person income and expenditure


On solving (1) * 7 & (2) * 9, we get

= > 63x - 28y = 14000

= > 63x - 27y = 18000

      ----------------------------

                  y = 4000


Substitute y = 4000 in (1), we get

= > 9x - 4y = 2000

= > 9x - 16000 = 2000

= > 9x = 18000

= > x = 2000


Therefore income of 1st person = 9 * 2000

                                                      = 18000



Therefore income of 2nd person = 7x

                                                        = 7 * 2000

                                                        = 14000.




Hope this helps!