Question

the ratio of the income of A and B is 2 : 3 and that of their expenditure is 1 : 2. If 905 of B's expenditure is equal to the income of A, then what is the ratio of savings of A and B​

Answer 1

Answer:

8 : 7

Step-by-step explanation:

Let Income of A = 2x

Let Income of A = 2xIncome of B = 3x

Let Income of A = 2xIncome of B = 3xSimilarly Let expenditure of A = y

Let Income of A = 2xIncome of B = 3xSimilarly Let expenditure of A = yExpenditure of B = 2y

Let Income of A = 2xIncome of B = 3xSimilarly Let expenditure of A = yExpenditure of B = 2yNow 90℅ of B expenditure = Income of A

i.e. 0.9 × 2y = 2x i.e 1.8y = 2x ...…(1)

…(1)We know Saving = Income - Expenditure

…(1)We know Saving = Income - ExpenditureSaving for A = 2x - y

…(1)We know Saving = Income - ExpenditureSaving for A = 2x - ySaving for B = 3x - 2y

…(1)We know Saving = Income - ExpenditureSaving for A = 2x - ySaving for B = 3x - 2yRatio of saving = (2x - y) : (3x - 2y)

…(1)We know Saving = Income - ExpenditureSaving for A = 2x - ySaving for B = 3x - 2yRatio of saving = (2x - y) : (3x - 2y)Using (1) = (1.8y - y) : (2.7y - 2y) = 0.8y : 0.7y = 8 : 7

…(1)We know Saving = Income - ExpenditureSaving for A = 2x - ySaving for B = 3x - 2yRatio of saving = (2x - y) : (3x - 2y)Using (1) = (1.8y - y) : (2.7y - 2y) = 0.8y : 0.7y = 8 : 7Hence Answer = 8 : 7

Answer 2

Ratio of savings of A and B is 1 : 1

Step-by-step explanation:

Let the income of A is x then the income of B will be,

$\frac{\text{Income of A}}{\text{Income of B}}=\frac{x}{x'}=\frac{2}{3}$

x' = $\frac{3}{2}x$

Let the expenditure of A = y then the expenditure of B will be,

$\frac{\text{Expenditure of A}}{\text{Expenditure of B}}=\frac{y}{y'}=\frac{1}{2}$

y' = 2y

Saving of A = (x - y)

Saving of B = ($\frac{3x}{2}-2y$)

If B's expenditure 905 is equal to the income of A then,

x = 2y = 905

x = 905 , y = 452.5

Now saving of A = x - y = 905 - 452.5 = 452.5

Income of B = $\frac{3}{2}\times 905=1357.5$

Saving of B = 1357.5 - 905 = 452.50

Now ratio of savings of A and B = $\frac{452.5}{452.5}=1:1$

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