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The ratio of incomes of P, Q and R is 3 : 7 : 4 and the ratio of their expenditures is 4 : 3 : 5. If P saves 14(2/7)% of his income, then find the ratio of the saving done by P, Q and R.
- a)4 : 5 : 1
- b)6 : 71 : 11
- c)8 : 61 : 13
- d)7 : 45 : 12
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The ratio of incomes of P, Q and R is 3 : 7 : 4 and the ratio of thei...
∵ The ratio of incomes of P, Q and R = 3 : 7 : 4
We can also write as:
Ratio of incomes = 3x : 7x : 4x
∵ The ratio of expenditures of P, Q and R = 4 : 3 : 5
We can also write as:
Ratio of expenditures = 4y : 3y : 5y
∴ Ratio of savings of P, Q & R = (3x – 4y) : (7x – 3y) : (4x – 5y)
∴ Ratio of savings of P, Q and R = (42 – 36) : (98 – 27) : (56 – 45) = 6 : 71 : 11
Hence, the correct option is (B).
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The ratio of incomes of P, Q and R is 3 : 7 : 4 and the ratio of thei...
Given:
The ratio of incomes of P, Q, and R is 3 : 7 : 4.
The ratio of their expenditures is 4 : 3 : 5.
P saves 14(2/7)% of his income.
To Find:
The ratio of the saving done by P, Q, and R.
Solution:
Step 1: Find the Incomes of P, Q, and R
Let the incomes of P, Q, and R be 3x, 7x, and 4x respectively.
So, the ratio of their incomes is 3x : 7x : 4x.
Step 2: Find the Expenditures of P, Q, and R
Let the expenditures of P, Q, and R be 4y, 3y, and 5y respectively.
So, the ratio of their expenditures is 4y : 3y : 5y.
Step 3: Find the Savings of P
P saves 14(2/7)% of his income.
Therefore, the savings of P = (14(2/7)/100) * 3x = 43x/100.
Step 4: Find the Savings of Q
The savings of Q can be found by multiplying the income of Q by the savings percentage of P.
Therefore, the savings of Q = (43x/100) * (7x/3x) = 301x^2/300.
Step 5: Find the Savings of R
The savings of R can be found by multiplying the income of R by the savings percentage of P.
Therefore, the savings of R = (43x/100) * (4x/3x) = 172x^2/300.
Step 6: Find the Ratio of the Savings
The ratio of the savings of P, Q, and R = (43x/100) : (301x^2/300) : (172x^2/300)
Simplifying this ratio, we get 43 : 301x/7 : 172x/4.
Step 7: Simplify the Ratio
To simplify the ratio, we multiply each term by the least common multiple (LCM) of 7 and 4, which is 28.
Therefore, the simplified ratio of the savings of P, Q, and R = 43*28 : (301x/7)*28 : (172x/4)*28
Simplifying this further, we get 1204 : 301x : 1196x.
Step 8: Verify the Options
Comparing the simplified ratio with the given options, we find that the ratio 6 : 71 : 11 matches the simplified ratio.
Hence, the correct answer is option B) 6 : 71 : 11.
The ratio of incomes of P, Q, and R is 3 : 7 : 4.
The ratio of their expenditures is 4 : 3 : 5.
P saves 14(2/7)% of his income.
To Find:
The ratio of the saving done by P, Q, and R.
Solution:
Step 1: Find the Incomes of P, Q, and R
Let the incomes of P, Q, and R be 3x, 7x, and 4x respectively.
So, the ratio of their incomes is 3x : 7x : 4x.
Step 2: Find the Expenditures of P, Q, and R
Let the expenditures of P, Q, and R be 4y, 3y, and 5y respectively.
So, the ratio of their expenditures is 4y : 3y : 5y.
Step 3: Find the Savings of P
P saves 14(2/7)% of his income.
Therefore, the savings of P = (14(2/7)/100) * 3x = 43x/100.
Step 4: Find the Savings of Q
The savings of Q can be found by multiplying the income of Q by the savings percentage of P.
Therefore, the savings of Q = (43x/100) * (7x/3x) = 301x^2/300.
Step 5: Find the Savings of R
The savings of R can be found by multiplying the income of R by the savings percentage of P.
Therefore, the savings of R = (43x/100) * (4x/3x) = 172x^2/300.
Step 6: Find the Ratio of the Savings
The ratio of the savings of P, Q, and R = (43x/100) : (301x^2/300) : (172x^2/300)
Simplifying this ratio, we get 43 : 301x/7 : 172x/4.
Step 7: Simplify the Ratio
To simplify the ratio, we multiply each term by the least common multiple (LCM) of 7 and 4, which is 28.
Therefore, the simplified ratio of the savings of P, Q, and R = 43*28 : (301x/7)*28 : (172x/4)*28
Simplifying this further, we get 1204 : 301x : 1196x.
Step 8: Verify the Options
Comparing the simplified ratio with the given options, we find that the ratio 6 : 71 : 11 matches the simplified ratio.
Hence, the correct answer is option B) 6 : 71 : 11.
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The ratio of incomes of P, Q and R is 3 : 7 : 4 and the ratio of their expenditures is 4 : 3 : 5. If P saves 14(2/7)% of his income, then find the ratio of the saving done by P, Q and R.a)4 : 5 : 1b)6 : 71 : 11c)8 : 61 : 13d)7 : 45 : 12e)None of theseCorrect answer is option 'B'. Can you explain this answer?
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