The monthly incomes of A, B and C are in the ratio 2 : 9 : 3 and their expenses are in the ratio 3 : 9 : 5. If A’s saving is half of his total income, then savings of A, B and C are, respectively, in the ratio of:

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Step 1: Let the incomes of A, B, and C be 2x, 9x, and 3x respectively.

Step 2: Expenses are in the ratio 3 : 9 : 5. Let their expenses be 3y, 9y, and 5y respectively.

Step 3: A’s saving is half of his income, so saving of A = (1/2) * 2x = x.

Step 4: Since saving = income - expenses, for A:
Saving_A = Income_A - Expense_A
x = 2x - 3y
=> 3y = 2x - x = x
=> y = x/3

Step 5: Calculate savings of B and C:
Saving_B = Income_B - Expense_B = 9x - 9y = 9x - 9(x/3) = 9x - 3x = 6x
Saving_C = Income_C - Expense_C = 3x - 5y = 3x - 5(x/3) = 3x - (5x/3) = (9x/3) - (5x/3) = 4x/3

Step 6: Savings ratio of A : B : C = x : 6x : 4x/3
= 1 : 6 : 4/3
Multiply all by 3 to clear denominator:
= 3 : 18 : 4

Therefore, the savings ratio is 3 : 18 : 4.

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