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The incomes of A, B, C are in the ratio of 12: 9 : 7 and their spendings are in the ratio 15 : 9 : 8. If A saves 25% if his income. What is the ratio of the savings of A,B and C ?
- a)3 : 1 : 11
- b)15 : 18 : 7
- c)15 : 18 : 11
- d)12 : 15 : 13
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 spendin...
Given: Incomes of A, B, C are in the ratio of 12: 9 : 7 and their spendings are in the ratio 15 : 9 : 8. A saves 25% of his income.
Let the incomes of A, B, C be 12x, 9x, and 7x respectively.
And, their spendings be 15y, 9y, and 8y respectively.
A saves 25% of his income = 25% of 12x = (25/100) * 12x = 3x
Therefore, A's spending = 15y, and A's saving = 3x.
Now, we can calculate the spending and savings of B and C as follows:
- Spending of B = 9y * 15/9 = 15y
- Spending of C = 7y * 15/8 = 13.125y
Let S be the total savings of A, B, and C.
Then, S = A's saving + B's saving + C's saving
S = 3x + (9x - 15y) + (7x - 13.125y)
Simplifying the above expression, we get:
S = 15x/8 - 2.125y
Now, we can express the ratio of savings of A, B, and C as:
A:B:C = 3x : (9x - 15y) : (7x - 13.125y)
To simplify this ratio, we can substitute the values of x and y as follows:
- x = k (let k be a constant)
- 15y = 15/32 * 12k = 45/8 k
Therefore, the ratio of savings of A, B, and C is:
A:B:C = 3k : 6k : 11k
Simplifying this ratio by dividing all terms by 3k, we get:
A:B:C = 1 : 2 : 11/3
Multiplying all terms by 3, we get:
A:B:C = 3 : 6 : 11
Hence, the ratio of the savings of A, B, and C is 15 : 18 : 11 (option C).
Let the incomes of A, B, C be 12x, 9x, and 7x respectively.
And, their spendings be 15y, 9y, and 8y respectively.
A saves 25% of his income = 25% of 12x = (25/100) * 12x = 3x
Therefore, A's spending = 15y, and A's saving = 3x.
Now, we can calculate the spending and savings of B and C as follows:
- Spending of B = 9y * 15/9 = 15y
- Spending of C = 7y * 15/8 = 13.125y
Let S be the total savings of A, B, and C.
Then, S = A's saving + B's saving + C's saving
S = 3x + (9x - 15y) + (7x - 13.125y)
Simplifying the above expression, we get:
S = 15x/8 - 2.125y
Now, we can express the ratio of savings of A, B, and C as:
A:B:C = 3x : (9x - 15y) : (7x - 13.125y)
To simplify this ratio, we can substitute the values of x and y as follows:
- x = k (let k be a constant)
- 15y = 15/32 * 12k = 45/8 k
Therefore, the ratio of savings of A, B, and C is:
A:B:C = 3k : 6k : 11k
Simplifying this ratio by dividing all terms by 3k, we get:
A:B:C = 1 : 2 : 11/3
Multiplying all terms by 3, we get:
A:B:C = 3 : 6 : 11
Hence, the ratio of the savings of A, B, and C is 15 : 18 : 11 (option C).
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Community Answer
The incomes of A, B, C are in the ratio of 12: 9 : 7 and their spendin...
Income = Expenditure + Savings
A 12x = 15 y + 3x
B 9x = 9y + (9x–9y)
C 7x = 8y + (7x – 8y)
Therefore, 12x – 3x = 15y
A 12x = 15 y + 3x
B 9x = 9y + (9x–9y)
C 7x = 8y + (7x – 8y)
Therefore, 12x – 3x = 15y
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The incomes of A, B, C are in the ratio of 12: 9 : 7 and their spendings are in the ratio 15 : 9 : 8. If A saves 25% if his income. What is the ratio of the savings of A,B and C ?a)3 : 1 : 11b)15 : 18 : 7c)15 : 18 : 11d)12 : 15 : 13Correct answer is option 'C'. Can you explain this answer?
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