Question

incomes of A B,C are in the ratio 1:2:3 while their expenditure are in the ratio 2:3:4 if A saves one third of his income , find the ratio of their savings​

Answer 1

Step-by-step explanation:

Given :-

Incomes of A B,C are in the ratio 1:2:3 while their expenditure are in the ratio 2:3:4 . A saves one third of his income.

To find :-

Find the ratio of their savings ?

Solution :-

Given that

The ratio of the incomes of

A,B and C = 1:2:3

Let they be Rs. X , Rs. 2X and Rs. 3X

The income of A = Rs. X

The income of B = Rs. 2X

The income of C = Rs. 3X

The ratio of the expenditures of

A, B and C = 2:3:4

Let they be Rs. 2Y , Rs. 3Y and Rs. 4Y

The expenditure of A = Rs. 2Y

The expenditure of B = Rs. 3Y

The expenditure of C = Rs. 4Y

We know that

Saving = Income - Expenditure

The saving of A = Income of A - Expenditure of A

=> The saving of A =Rs. ( X-2Y )

According to the given problem

The saving of A = 1/3 of the income of A

X-2Y = (1/3) of X

=> X-2Y = (1/3)×X

=> X-2Y = (1×X)/3

=> X-2Y = X/3

=> 3(X-2Y) = X

=> 3X-6Y = X

=> 3X-X = 6Y

=> 2X = 6Y

=> X/Y = 6/2

=> X/Y = 3/1

=> X/Y = 3

=> X = 3Y -------------(1)

Now,

Saving of A = Income of A - Expenditure of A

=> X-2Y

=> 3Y-2Y (From (1))

=> Y

The saving of A = Y

The saving of B = Income of B - Expenditure of B

The saving of B = 2X-3Y

=> The saving of B = 2(3Y)-3Y

=> The saving of B = 6Y-3Y

The saving of B = 3Y

The saving of C = Income of C - Expenditure of C

=> The saving of C = 3X-4Y

=> The saving of C = 3(3Y)-4Y

=> The saving of C = 9Y-4Y

The saving of C = 5Y

The ratio of the savings of A , B and C

=> Y : 3Y : 5Y

=> 1:3:5

Answer:-

The ratio of the savings of A,B and C is 1:3:5

Used formulae:-

→ Saving = Income - Expenditure

Answer 2

Given :

• Incomes of A B,C are in the ratio 1:2:3

• Expenditure of A B,C are in the ratio 2:3:4

Condition :

• A saves one third of his income

To Find :

• The ratio of their savings

Hints :

• 1) The ratio of their expenditure is to be calculated

• 2) Then we have to assume that Incomes of A B,C are 1x, 2x and 3x and Expenditure of A B,C are in 2y, 3y and 4y

Solution :

Let Incomes of A B,C are 1x, 2x and 3x and Expenditure of A B,C are in 2y, 3y and 4y

$\rm \: \therefore Income = 1x :2x : 3x$

$\rm \: \therefore \: Expenditure = 2y :3y:4y$

Then,

$\rm \: \therefore \: Saving= (x - 2y) : (2x - 3y) : (3x - 4y)$

According to the condition given in question,

$\rm \: \implies \: x - 2y = \dfrac{x}{3}$

$\rm \implies \: 3x - 6y = x$

$\rm \implies \: 2x = 6y$

$\rm \implies\: x = 3y$

So,

Ratio of savings,

$\rm \therefore \: (3y - 2y) : (6y - 3y) : (9y - 4y)$

$\rm \implies \: y : 3y : 5y$

$\rm \therefore \huge\boxed{1 : 3 : 5}$