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Incomes of X and Y are in the ratio 7 ∶ 8. Their expenditures are in the ratio 4 ∶ 5. If both individually save Rs. 960 at the end of the month, then what is the income (in Rs) of X?
- a)2240
- b)2560
- c)1280
- d)1600
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Incomes of X and Y are in the ratio 7 ∶ 8. Their expenditures ar...
Let the incomes of X and Y be 7a and 8a
Let the expenditures of X and Y be 4b and 5b.
Then the income of both will be,
⇒ 7a = 4b + 960 ----(1)
⇒ 8a = 5b + 960 ----(2)
By solving the above equation, we get
a = 320 and b = 320
The income of X = 7a = 7 × 320 = 2240.
Most Upvoted Answer
Incomes of X and Y are in the ratio 7 ∶ 8. Their expenditures ar...
Ratio of incomes and expenditures
The given problem states that the incomes of X and Y are in the ratio 7:8, and their expenditures are in the ratio 4:5.
Let's assume the incomes of X and Y to be 7x and 8x respectively, and their expenditures to be 4y and 5y respectively.
Savings of X and Y
According to the problem, both X and Y save Rs. 960 at the end of the month.
Now, we can calculate the savings of X and Y as follows:
Savings of X = Income of X - Expenditure of X
= 7x - 4y
Savings of Y = Income of Y - Expenditure of Y
= 8x - 5y
Given that both X and Y save Rs. 960, we have:
7x - 4y = 960 ...(1)
8x - 5y = 960 ...(2)
Solving the equations
To find the value of x, we need to solve the above two equations.
Multiplying equation (1) by 8 and equation (2) by 7, we get:
56x - 32y = 7680 ...(3)
56x - 35y = 6720 ...(4)
Subtracting equation (4) from equation (3), we have:
56x - 35y - (56x - 32y) = 7680 - 6720
-35y + 32y = 960
-3y = 960
y = -960/3
y = -320
Substituting the value of y in equation (1), we can find the value of x:
7x - 4(-320) = 960
7x + 1280 = 960
7x = 960 - 1280
7x = -320
x = -320/7
Since income cannot be negative, we can conclude that the value of x is positive.
Therefore, the income of X, which is 7x, is:
7x = 7 * (-320/7)
= -320
However, as mentioned earlier, income cannot be negative. Therefore, there might be an error in the given problem or in the calculations.
In conclusion, it is not possible to determine the income of X based on the given information.
The given problem states that the incomes of X and Y are in the ratio 7:8, and their expenditures are in the ratio 4:5.
Let's assume the incomes of X and Y to be 7x and 8x respectively, and their expenditures to be 4y and 5y respectively.
Savings of X and Y
According to the problem, both X and Y save Rs. 960 at the end of the month.
Now, we can calculate the savings of X and Y as follows:
Savings of X = Income of X - Expenditure of X
= 7x - 4y
Savings of Y = Income of Y - Expenditure of Y
= 8x - 5y
Given that both X and Y save Rs. 960, we have:
7x - 4y = 960 ...(1)
8x - 5y = 960 ...(2)
Solving the equations
To find the value of x, we need to solve the above two equations.
Multiplying equation (1) by 8 and equation (2) by 7, we get:
56x - 32y = 7680 ...(3)
56x - 35y = 6720 ...(4)
Subtracting equation (4) from equation (3), we have:
56x - 35y - (56x - 32y) = 7680 - 6720
-35y + 32y = 960
-3y = 960
y = -960/3
y = -320
Substituting the value of y in equation (1), we can find the value of x:
7x - 4(-320) = 960
7x + 1280 = 960
7x = 960 - 1280
7x = -320
x = -320/7
Since income cannot be negative, we can conclude that the value of x is positive.
Therefore, the income of X, which is 7x, is:
7x = 7 * (-320/7)
= -320
However, as mentioned earlier, income cannot be negative. Therefore, there might be an error in the given problem or in the calculations.
In conclusion, it is not possible to determine the income of X based on the given information.
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Community Answer
Incomes of X and Y are in the ratio 7 ∶ 8. Their expenditures ar...
Let the income be x.
Then income of X is 7x and of Y is 8x.
Then expenditure of X is 4x and Y is 5x.
If X and Y save Rs. 960 individually then
7x-4x=960 and 8x-5x=960
solving them
3x=960
x=320
then income of X will be 7×320=2240. Answer
Then income of X is 7x and of Y is 8x.
Then expenditure of X is 4x and Y is 5x.
If X and Y save Rs. 960 individually then
7x-4x=960 and 8x-5x=960
solving them
3x=960
x=320
then income of X will be 7×320=2240. Answer
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Incomes of X and Y are in the ratio 7 ∶ 8. Their expenditures are in the ratio 4 ∶ 5. If both individually save Rs. 960 at the end of the month, then what is the income (in Rs) of X?a)2240b)2560c)1280d)1600Correct answer is option 'A'. Can you explain this answer?
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Incomes of X and Y are in the ratio 7 ∶ 8. Their expenditures are in the ratio 4 ∶ 5. If both individually save Rs. 960 at the end of the month, then what is the income (in Rs) of X?a)2240b)2560c)1280d)1600Correct answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Incomes of X and Y are in the ratio 7 ∶ 8. Their expenditures are in the ratio 4 ∶ 5. If both individually save Rs. 960 at the end of the month, then what is the income (in Rs) of X?a)2240b)2560c)1280d)1600Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Incomes of X and Y are in the ratio 7 ∶ 8. Their expenditures are in the ratio 4 ∶ 5. If both individually save Rs. 960 at the end of the month, then what is the income (in Rs) of X?a)2240b)2560c)1280d)1600Correct answer is option 'A'. Can you explain this answer?.
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