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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?
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Most Upvoted Answer
The incomes of A, B, C are in the ratio of 12: 9: 7 and their spending...
Given:
Incomes ratio of A: B: C = 12: 9: 7
Spending ratio of A: B: C = 15: 9: 8
A saves 25% of his income
To find:
Ratio of savings of A, B, and C
Solution:
Let the incomes of A, B, and C be 12x, 9x, and 7x respectively.
And, let the spending of A, B, and C be 15y, 9y, and 8y respectively.
Since A saves 25% of his income, his savings would be 25% of 12x = 3x
Now, the remaining income of A after savings = 12x - 3x = 9x
The savings of B and C can be found by subtracting their spending from their incomes.
Savings of B = 9x - 9y = x(9 - y)
Savings of C = 7x - 8y = x(7 - 8/3y)
Now, we can find the ratio of savings of A, B, and C as follows:
Ratio of savings of A, B, and C = 3x : x(9 - y) : x(7 - 8/3y)
Simplifying the ratio, we get:
Ratio of savings of A, B, and C = 3 : 3(9 - y)/x : 3(7 - 8/3y)/x
Ratio of savings of A, B, and C = 3 : 27/4 - 3y/4 : 21/4 - 2y/3
Multiplying the ratio by 4 to eliminate fractions, we get:
Ratio of savings of A, B, and C = 12 : 27 - 3y : 21 - 8y/3
Multiplying the ratio by 3 to eliminate fractions, we get:
Ratio of savings of A, B, and C = 36 : 81 - 9y : 63 - 8y
Ratio of savings of A, B, and C = 36 : 81 : 63 - 8y + 9y
Ratio of savings of A, B, and C = 36 : 81 : 63 + y
Given that the incomes ratio of A, B, and C are in the ratio 12: 9: 7
Thus, we can take y = 7x/8 and substitute in the ratio of savings.
Ratio of savings of A, B, and C = 36 : 81 : 63 + 7x/8
Ratio of savings of A, B, and C = 36 : 81 : 135/8
Multiplying the ratio by 8 to eliminate fractions, we get:
Ratio of savings of A, B, and C = 288 : 648 : 135
Simplifying the ratio, we get:
Ratio of savings of A, B, and C = 16 : 36 : 7
Hence, the ratio of savings of A, B, and C is 15:18:11.
Incomes ratio of A: B: C = 12: 9: 7
Spending ratio of A: B: C = 15: 9: 8
A saves 25% of his income
To find:
Ratio of savings of A, B, and C
Solution:
Let the incomes of A, B, and C be 12x, 9x, and 7x respectively.
And, let the spending of A, B, and C be 15y, 9y, and 8y respectively.
Since A saves 25% of his income, his savings would be 25% of 12x = 3x
Now, the remaining income of A after savings = 12x - 3x = 9x
The savings of B and C can be found by subtracting their spending from their incomes.
Savings of B = 9x - 9y = x(9 - y)
Savings of C = 7x - 8y = x(7 - 8/3y)
Now, we can find the ratio of savings of A, B, and C as follows:
Ratio of savings of A, B, and C = 3x : x(9 - y) : x(7 - 8/3y)
Simplifying the ratio, we get:
Ratio of savings of A, B, and C = 3 : 3(9 - y)/x : 3(7 - 8/3y)/x
Ratio of savings of A, B, and C = 3 : 27/4 - 3y/4 : 21/4 - 2y/3
Multiplying the ratio by 4 to eliminate fractions, we get:
Ratio of savings of A, B, and C = 12 : 27 - 3y : 21 - 8y/3
Multiplying the ratio by 3 to eliminate fractions, we get:
Ratio of savings of A, B, and C = 36 : 81 - 9y : 63 - 8y
Ratio of savings of A, B, and C = 36 : 81 : 63 - 8y + 9y
Ratio of savings of A, B, and C = 36 : 81 : 63 + y
Given that the incomes ratio of A, B, and C are in the ratio 12: 9: 7
Thus, we can take y = 7x/8 and substitute in the ratio of savings.
Ratio of savings of A, B, and C = 36 : 81 : 63 + 7x/8
Ratio of savings of A, B, and C = 36 : 81 : 135/8
Multiplying the ratio by 8 to eliminate fractions, we get:
Ratio of savings of A, B, and C = 288 : 648 : 135
Simplifying the ratio, we get:
Ratio of savings of A, B, and C = 16 : 36 : 7
Hence, the ratio of savings of A, B, and C is 15:18:11.
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Community Answer
The incomes of A, B, C are in the ratio of 12: 9: 7 and their spending...
Let income be X
Incomes are :A: 12/28 X; B: 9/28X; C: 7/28X
Let Spent be Y
Spent is:
A: 15/32 Y; B: 9/32 Y; C: 8/32 Y
Solving these equations we get the value of Y in terms of X
Y=24/35 X
Find the values of spent in terms of X
A: 9/28 X; B: 27/140 X; C: 6/35 X
subtract the values of spent from the incomes
taking the ratio of the obtained values gives us the answer
taking the ratio of the obtained values gives us the answer
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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?
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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 UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC 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 UPSC 2024 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?.
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 UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC 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 UPSC 2024 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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ample number of questions to practice 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? tests, examples and also practice UPSC tests.
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