Question
Download Solution PDFThe ratio of the incomes of A and B is 3 : 5 and the ratio of their expenditures is 2 : 3. If the income of A is equal to
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ratio of incomes of A and B = 3 : 5
Ratio of expenditures of A and B = 2 : 3
Income of A is equal to 6/7 of the expenditure of B.
Calculation:
Let the income of A be 3x and the income of B be 5x.
Let the expenditure of A be 2y and the expenditure of B be 3y.
From the third condition, "Income of A is equal to 6/7 of the expenditure of B":
Income of A = (6/7) × Expenditure of B
3x = (6/7) × 3y
3x = 18y / 7
x = 6y / 7
Income of A = 3x = 3 × (6y/7) = 18y/7
Income of B = 5x = 5 × (6y/7) = 30y/7
Expenditure of A = 2y
Expenditure of B = 3y
Savings of A = Income of A - Expenditure of A
= (18y/7) - 2y
= (18y - 14y) / 7
= 4y/7
Savings of B = Income of B - Expenditure of B
= (30y/7) - 3y
= (30y - 21y) / 7
= 9y/7
Ratio of Savings (A : B) = (4y/7) : (9y/7)
= 4y : 9y = 4 : 9
∴ The correct answer is option 4.
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