Question

The incomes of A and B are
in the ratio 3:2 and their
expenditure in the ratio 5:3.If
each saves Rs 1500 then B's
income is : *​

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The incomes of A and B are in the ratio 3:2

• Their expenditure is in the ratio 5 : 3

• The savings of each of them is Rs. 1500

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The income of B.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the common ratio of incomes of A and B be x

Income of A = 3x

Income of B = 2x

Let the common ratio of expenditure be y

Expenditure of A = 5y

Expenditure of B = 3y

As the savings of each of them is Rs.1000

Therefore:-

$\rm \implies3x - 5y = 1000....(i)$

$\rm \implies2x - 3y = 1000....(ii)$

Multiplying equation (i) with 2

= 2(3x - 5y = 1000)

= 6x - 10y = 2000...….(iii)

Multiplying equation (ii) with 3

= 3(2x - 3y = 1000)

= 6x - 9y = 3000....….(iv)

Subtracting (iii) from (iv)

$\rm \implies6x - 9y - (6x - 10y) = 3000 - 2000$

$\rm \implies6x - 9y - 6x + 10y= 1000$

$\rm \implies y= 1000$

Substituting y = 1000 in equation (i)

➝ 3x - 5y = 1000

➝ 3x - 5(1000) = 1000

➝ 3x = 1000 + 5000

➝ 3x = 6000

➝ x = 2000

Income of B

= 2x

= 2 × 2000

= 4000

$\underline{ \boxed{ \therefore\rm Income \: of \: B= Rs.4000}}$

Answer 2

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$\huge\red{\underline{{\bf Question : }}}$

• The incomes of A and B are in the ratio 3:2 and their expenditure in the ratio 5:3.If each saves Rs 1500 then B's income is?

$\huge\red{\underline{{\bf Answer : }}}$

$\large\bf{\underline\blue{Given:}}$

• The incomes of A and B are in the ratio = 3:2

• Their expenditure are in the ratio = 5:3.

• The savings of each of them = Rs. 1500

$\large\bf{\underline\green{To Find:}}$

• The income of B.

$\large\bf{\underline\orange{Solution:}}$

• Let the income of A be 3x

• Let the income of B be 2x

• Their expenditure be 5y and 3y.

▪️According to the question :-

$\sf\pink{⟹ 3x - 5y = 1000} \: - - - (1)$

$\sf\pink{⟹2x - 3y = 1000} \: - - -(2)$

▪️Now we multiply the equation ( 1 ) by 3 and ( 2 ) by 5.

$\sf\pink{⟹9x - 15y = 3000} \: - - - (3)$

$\sf\pink{⟹10x - 15y = 5000} \: - - - (4)$

$\sf\pink{⟹x = 2000}$

▪️[ Subtract equation ( 3 ) from equation ( 4 ) ]

▪️Then income of A = 3x = Rs. ( 3 × 2000 ) = Rs. 6000.

${\boxed{{\bf\red{➭ \: Income \: of \: B = \: Rs. 6000}}}}$

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