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The incomes of A, B, C are in the ratio of 12: 9: 7 and their spending are in the ratio 15: 9: 8. If A saves 25% of his income. What is the ratio of the savings of A, B and C respectively?
  • a)
    12: 15: 19
  • b)
    11: 15: 18
  • c)
    15: 18: 11
  • d)
    21: 24: 29
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The incomes of A, B, C are in the ratio of 12: 9: 7 and their spending...
Given:
Incomes of A, B, C are in the ratio of 12: 9: 7
Spending of A, B, C are in the ratio of 15: 9: 8
A saves 25% of his income.

To find:
The ratio of the savings of A, B, and C.

Solution:
Let's assume the incomes of A, B, and C as 12x, 9x, and 7x respectively.
And let's assume the spending of A, B, and C as 15y, 9y, and 8y respectively.

A saves 25% of his income, so the savings of A can be calculated as:
Savings of A = 25% of Income of A
= (25/100) * 12x
= 3x

Now, let's calculate the savings of B and C:
Given that the income of B is 9x and the spending of B is 9y.
The savings of B can be calculated as:
Savings of B = Income of B - Spending of B
= 9x - 9y
= 9(x - y)

Similarly, the savings of C can be calculated as:
Savings of C = Income of C - Spending of C
= 7x - 8y

Now, let's find the ratio of the savings of A, B, and C:
Ratio of the savings of A, B, and C = Savings of A : Savings of B : Savings of C
= 3x : 9(x - y) : 7x - 8y
= 3x : 9x - 9y : 7x - 8y

Simplifying the ratio:
We can multiply each term in the ratio by a common factor of 1/x to simplify it further.

Ratio of the savings of A, B, and C = 3x : 9x - 9y : 7x - 8y
= 3 : 9 - 9(y/x) : 7 - 8(y/x)
= 3 : 9 - 9(15/12) : 7 - 8(15/12)
= 3 : 9 - 9(5/4) : 7 - 8(5/4)
= 3 : 9 - 45/4 : 7 - 40/4
= 3 : (9 - 45/4) : (7 - 40/4)
= 3 : (36/4 - 45/4) : (28/4 - 40/4)
= 3 : (-9/4) : (-12/4)
= 3 : (-9/4) : (-3)

Since the ratio cannot have negative values, we can multiply each term in the ratio by -1 to make it positive without changing the ratio.

Ratio of the savings of A, B, and C = 3 : (-9/4) : (-3)
= 3 : (9/4) : 3
= 12 : 9 : 16

Therefore, the ratio of the savings of A, B, and C is 12: 9:
Free Test
Community Answer
The incomes of A, B, C are in the ratio of 12: 9: 7 and their spending...
Let the income be 12x, 9x, 7x and expenditure is 15y, 9y, 8y.
Income – Expenditure = Savings
For A, 12x -15y = 25% of 12x = 3x  9x =15y  => y = 3x/5  B’s
Saving = 9x - 9y  => 9x-9(3x/5) => 18x/5
C’s Saving = 7x-8y => 7x – 8(3x/5) => 11x/5
Savings Ratio A: B: C :: 3x: 18x/5: 11x/5
Required ratio = 15: 18: 11 
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The incomes of A, B, C are in the ratio of 12: 9: 7 and their spending are in the ratio 15: 9: 8. If A saves 25% of his income. What is the ratio of the savings of A, B and C respectively?a)12: 15: 19b)11: 15: 18c)15: 18: 11d)21: 24: 29Correct answer is option 'C'. Can you explain this answer? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about The incomes of A, B, C are in the ratio of 12: 9: 7 and their spending are in the ratio 15: 9: 8. If A saves 25% of his income. What is the ratio of the savings of A, B and C respectively?a)12: 15: 19b)11: 15: 18c)15: 18: 11d)21: 24: 29Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The incomes of A, B, C are in the ratio of 12: 9: 7 and their spending are in the ratio 15: 9: 8. If A saves 25% of his income. What is the ratio of the savings of A, B and C respectively?a)12: 15: 19b)11: 15: 18c)15: 18: 11d)21: 24: 29Correct answer is option 'C'. Can you explain this answer?.
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