Question

The ratio of inc incomes of two persons is 9:7 and the ratio of their expenditures is 4:3 .If each of them manages to save ₹2000 per month, find their monthly income

Answer 1

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Answer 2

Answer:

Monthly income of first person = Rs. 18000

Monthly income of second person = Rs. 14000

Step-by-step explanation:

Let the common ratio term for incomes be x and for the expenditure be y.

So, the income of two persons will be 9·x and 7·x and their expenditure will be 4·y and 3·y respectively.

So, According to given condition

9·x - 4·y = 2000   .............(1)

7·x - 3·y = 2000    ............(2)

So from equation (1)

$x=\frac{(2000+4y)}{9}...........(3)\\\\\text{Putting this value of x in equation (2) }\\\\\implies 7\cdot \frac{(2000+4y)}{9}-3\cdot y=2000\\\\\implies \frac{(14000+28y)}{9}-3\cdot y=2000\\\\\implies \frac{(14000+28\cdot y-27\cdot y)}{9}=2000\\\\\implies y+14000=18000\\\\\implies y=4000\\\\\text{Now, putting value of y in equation (3)}\\\\\implies x=\frac{(2000+4\times 4000)}{9}\\\\\implies x=\frac{(2000+16000)}{9}\\\\\implies x=\frac{18000}{9}\\\\\implies x=2000$

So, Monthly income of first person = 9 × 2000 = Rs. 18000

and Monthly income of second person = 7 × 2000 = Rs. 14000