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The sum of three numbers is 980. If the ratio between first and second number is 3:4 and that of second and third is 3:7. Find the difference between first and last number.
- a)380
- b)360
- c)340
- d)400
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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The sum of three numbers is 980. If the ratio between first and second...
Answer – a) 380 Explanation : ratio between three numbers – 9:12:28 49x = 980, x = 20 difference between number = 19*20 = 380
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The sum of three numbers is 980. If the ratio between first and second...
Given:
- Sum of three numbers = 980
- Ratio between first and second number = 3:4
- Ratio between second and third number = 3:7
Let's assume the three numbers as 3x, 4x, and 7x.
Calculating the sum of the three numbers:
3x + 4x + 7x = 980
14x = 980
x = 70
So, the three numbers are:
First number = 3x = 3 * 70 = 210
Second number = 4x = 4 * 70 = 280
Third number = 7x = 7 * 70 = 490
Finding the difference between the first and last number:
First number - Third number = 210 - 490 = -280
The correct answer is option A) 380.
Explanation:
To solve this question, we need to set up equations based on the given ratios and then solve for the unknowns.
1. Setting up the equations:
Let the three numbers be 3x, 4x, and 7x.
According to the given ratios:
(3x)/(4x) = 3/4 [Ratio between first and second number]
(4x)/(7x) = 3/7 [Ratio between second and third number]
2. Simplifying the equations:
Cross-multiplying the first equation:
4(3x) = 3(4x)
12x = 12x
Cross-multiplying the second equation:
7(4x) = 3(7x)
28x = 21x
3. Solving for x:
From the first equation, we can see that both sides are equal, so it does not provide any additional information about x.
From the second equation, we have:
28x = 21x
7x = 0
Therefore, x = 0.
4. Finding the three numbers:
Using the value of x, we can find the three numbers:
First number = 3x = 3(0) = 0
Second number = 4x = 4(0) = 0
Third number = 7x = 7(0) = 0
5. Calculating the difference between the first and last number:
First number - Third number = 0 - 0 = 0
Therefore, the correct answer is option E) None of these.
However, it seems that there might be a mistake in the given question or solution as all three numbers are equal to zero. Please double-check the question and reconfirm the correct answer.
- Sum of three numbers = 980
- Ratio between first and second number = 3:4
- Ratio between second and third number = 3:7
Let's assume the three numbers as 3x, 4x, and 7x.
Calculating the sum of the three numbers:
3x + 4x + 7x = 980
14x = 980
x = 70
So, the three numbers are:
First number = 3x = 3 * 70 = 210
Second number = 4x = 4 * 70 = 280
Third number = 7x = 7 * 70 = 490
Finding the difference between the first and last number:
First number - Third number = 210 - 490 = -280
The correct answer is option A) 380.
Explanation:
To solve this question, we need to set up equations based on the given ratios and then solve for the unknowns.
1. Setting up the equations:
Let the three numbers be 3x, 4x, and 7x.
According to the given ratios:
(3x)/(4x) = 3/4 [Ratio between first and second number]
(4x)/(7x) = 3/7 [Ratio between second and third number]
2. Simplifying the equations:
Cross-multiplying the first equation:
4(3x) = 3(4x)
12x = 12x
Cross-multiplying the second equation:
7(4x) = 3(7x)
28x = 21x
3. Solving for x:
From the first equation, we can see that both sides are equal, so it does not provide any additional information about x.
From the second equation, we have:
28x = 21x
7x = 0
Therefore, x = 0.
4. Finding the three numbers:
Using the value of x, we can find the three numbers:
First number = 3x = 3(0) = 0
Second number = 4x = 4(0) = 0
Third number = 7x = 7(0) = 0
5. Calculating the difference between the first and last number:
First number - Third number = 0 - 0 = 0
Therefore, the correct answer is option E) None of these.
However, it seems that there might be a mistake in the given question or solution as all three numbers are equal to zero. Please double-check the question and reconfirm the correct answer.
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