if the ratio of the incomes of two persons is 9 : 7 and ratio of their expenditures is 4 : 3. Each of them saves Rs. 2000 per month. Find their monthly income.

You can solve this by using a system of equations.

Ratios imply that the actual numbers are probably larger than the numbers in the ratio, but that they are multiplied by a common factor. Call x the factor by which their incomes will by multiplied and call y the factor by which their expenditures will be multiplied.

income - expenditures = savings

9x - 4x = 2000

7x - 3x = 2000

this shows that both people end up with $2000 savings.

Now to solve, mulitply the top equation by 3 and the bottom equation by -4:

3(9x - 4x = 2000)

-4(7x - 3x = 2000)

27x - 12x = 6000

-28x 12x = -8000

Add them:

-x = -2000

so x = 2000

Now multiply both 9 and 7 by 2000 to get their monthly incomes:

9*2000 = $18000

7*2000 = $14000

Those are your answers.

You can proceed to solve for y and check your answer.

You should get y=4000

so 18000 - 4(4000) = 18000 - 16000 = 2000

and 14000 - 3(4000) = 14000 - 12000 = 2000

Yay!

Let the smaller income be x. Then the larger income is (9/7) x. Let the smaller expenditure be y. Then the larger expenditure is (4/3) y. Then we get these equations:

For the larger income:

(9/7) x - (4/3) y = 2000

21 [(9/7) x - (4/3) y] = 21 (2000)

*** 27x - 28y = 42000.

For the smaller income:

x - y = 2000 ---

## Tuesday, July 13, 2010

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