Question

Q6. The ratio of income of two persons is 11: 7 and the ratio of their expenditure is 9: 5. If each of them manage to save Rs. 400 per month, find their monthly incomes.​

Answer 1

Answer:

Let their salaries be 9x and 7x.

Let their expenditure be 4y and 3y.

According to the question,

9x−4y=2000 —(1)

7x−3y=2000 —(2)

From (1)

x=

9

2000+4y

—(3)

On putting x in (2), we get

7×

9

(2000+4y)

−3y=2000

9

(14000+28y)

−3y=2000

9

14000+28y−27y

=2000

14000+y=18000

y=4000

Now, put y in (3)

x=

9

2000+4×4000

x=

9

2000+16000

x=

9

18000

=2000

So,

Salary of first person =9×2000=Rs. 18000

Salary of second person =7×2000=Rs. 14000

Hence, this is the answer.

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

The ratio of income of two persons is 11 : 7

Let assume that,

Income of first person be 11x

and

Income of second person be 7y.

Also, Given that

The ratio of expenditure of two persons is 9 : 5

Let assume that,

Expenditure of first person be 9y

and

Expenditure of second person be 5y.

Further, given that, each of them manage to save Rs 400 per month.

We know,

$\boxed{ \bf{ \: \: \: \: Savings = Income - Expenditure \: \: \: \: }}$

So,

We get

$\rm :\longmapsto\:11x - 9y = 400 - - - (1)$

and

$\rm :\longmapsto\:7x - 5y = 400 - - - (2)$

So, On equating equation (1) and (2), we get

$\rm :\longmapsto\:7x - 5y = 11x - 9y$

$\rm :\longmapsto\:7x - 11x = 5y - 9y$

$\rm :\longmapsto\: - 4x = - 4y$

$\bf\implies \:x = y - - - (3)$

On substituting the value of x in equation (2), we get

$\rm :\longmapsto\:7y - 5y = 400$

$\rm :\longmapsto\:2y = 400$

$\bf\implies \:y = 200$

So,

$\bf\implies \:x = 200$

Hence,

Income of first person be 11x = 11 × 200 = Rs 2200

and

Income of second person be 7y = 7 × 200 = Rs 1400