Question

The income of two persons A and B are in the ratio 3:4 . If each saves Rs.100 per month,the ratio of their expenditures is 1:2.find their incomes ?​

Answer 1

Answer:-

Given:

Income of A and B are in the ratio 3 : 4.

Let the incomes of A and B be 3x , 4x.

And,

Savings of A & B each = ₹ 100

Expenditures are in the ratio 1 : 2.

So, Let the expenses of A & B be y , 2y.

We know that,

Income - Expenditure = Savings

So,

For A,

Income of A - Expenditure of A = Savings of A.

⟹ 3x - y = 100 -- equation (1)

For B,

Income of B - Expenditure of B = Savings of B

⟹ 4x - 2y = 100

⟹ 2(2x - y) = 100

⟹ 2x - y = 50 -- equation (2)

Subtract equation (2) from (1).

⟹ 3x - y - (2x - y) = 100 - 50

⟹ 3x - y - 2x + y = 50

⟹ x = 50

∴

• Income of A = 3x = 3(50) = ₹ 150

• Income of B = 4x = 4(50) = ₹ 200

Answer 2

Answer:

$\huge \bf \: given$

The income of two persons A and B are in the ratio 3:4 . If each saves Rs.100 per month,the ratio of their expenditures is 1:2.find their incomes ?

$\huge \bf \: to \: find$

Their incomes

$\huge \bf \: solution$

$\small \sf \green {let}$

$\sf income \: = \: 3 \ratio \: 4 = 3x \ratio \: 4x$

$\sf \: expenditure \: = 1 \ratio \: 2 =1 y \ratio \: 2y$

$\sf \: saving \: of \: and \: b \: = 100$

Now,

We know that

$\sf \: income \: - expenditure \: = saving$

For person A

$\sf \: 3x - y = 100 ... equation 1$

For person B

$\sf4x - 2y = 100$

$\sf \: 2(2x - y) = 100$

$\sf \: 3x - y - 2x + y = 50$

$\sf2x - y = 50 \: ...equation \: 2$

Now,

We will subtract equation 2 From 1

$\sf3x - y-(2x - y) = 100 \: - 50$

$\sf \: 3x - y - 2x + y = 50$

$\sf \: x = 50$

Now,

Person A - 3 × 50

Person B - 4 × 50

$\huge \fbox {person \: a \: = 150}$

$\huge \fbox {person \: b \: = 200}$