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The income of riya and priya are in the ratio of 4:5 and their expenditure is in the ratio of 2:3. If each of them saves 2000, then find their income.
- a)4000, 6000
- b)4000, 5000
- c)5000, 4000
- d)5000, 6000
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The income of riya and priya are in the ratio of 4:5 and their expendi...
Answer – b) 4000, 5000 Explanation : 4x – 2y = 2000 and 5x – 3y = 2000.
X = 1000, so income = 4000 and 5000
X = 1000, so income = 4000 and 5000
Most Upvoted Answer
The income of riya and priya are in the ratio of 4:5 and their expendi...
Given:
Income ratio of Riya and Priya = 4:5
Expenditure ratio of Riya and Priya = 2:3
Savings of each = $2000
To find:
Income of Riya and Priya
Solution:
Let the income of Riya be 4x and the income of Priya be 5x.
Let the expenditure of Riya be 2y and the expenditure of Priya be 3y.
Since the savings of each is $2000, we can write the equation as:
4x - 2y = 2000 ...(1)
5x - 3y = 2000 ...(2)
Now, we need to solve these two equations to find the values of x and y.
Simplifying equation (1) by dividing both sides by 2, we get:
2x - y = 1000
Multiplying equation (2) by 2, we get:
10x - 6y = 4000
Now, we have two equations:
2x - y = 1000 ...(3)
10x - 6y = 4000 ...(4)
Multiplying equation (3) by 6 and equation (4) by 1, we get:
12x - 6y = 6000 ...(5)
10x - 6y = 4000 ...(6)
Now, subtracting equation (6) from equation (5), we get:
(12x - 6y) - (10x - 6y) = 6000 - 4000
2x = 2000
x = 1000
Substituting the value of x in equation (1), we can find y:
4x - 2y = 2000
4(1000) - 2y = 2000
4000 - 2y = 2000
-2y = -2000
y = 1000
Therefore, the income of Riya is 4x = 4(1000) = $4000 and the income of Priya is 5x = 5(1000) = $5000.
Hence, the correct answer is option B) 4000, 5000.
Income ratio of Riya and Priya = 4:5
Expenditure ratio of Riya and Priya = 2:3
Savings of each = $2000
To find:
Income of Riya and Priya
Solution:
Let the income of Riya be 4x and the income of Priya be 5x.
Let the expenditure of Riya be 2y and the expenditure of Priya be 3y.
Since the savings of each is $2000, we can write the equation as:
4x - 2y = 2000 ...(1)
5x - 3y = 2000 ...(2)
Now, we need to solve these two equations to find the values of x and y.
Simplifying equation (1) by dividing both sides by 2, we get:
2x - y = 1000
Multiplying equation (2) by 2, we get:
10x - 6y = 4000
Now, we have two equations:
2x - y = 1000 ...(3)
10x - 6y = 4000 ...(4)
Multiplying equation (3) by 6 and equation (4) by 1, we get:
12x - 6y = 6000 ...(5)
10x - 6y = 4000 ...(6)
Now, subtracting equation (6) from equation (5), we get:
(12x - 6y) - (10x - 6y) = 6000 - 4000
2x = 2000
x = 1000
Substituting the value of x in equation (1), we can find y:
4x - 2y = 2000
4(1000) - 2y = 2000
4000 - 2y = 2000
-2y = -2000
y = 1000
Therefore, the income of Riya is 4x = 4(1000) = $4000 and the income of Priya is 5x = 5(1000) = $5000.
Hence, the correct answer is option B) 4000, 5000.
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Community Answer
The income of riya and priya are in the ratio of 4:5 and their expendi...
Answer – b) 4000, 5000 Explanation : 4x – 2y = 2000 and 5x – 3y = 2000.
X = 1000, so income = 4000 and 5000
X = 1000, so income = 4000 and 5000
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