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The ratio between two numbers is 7:5. If 5 is subtracted from each of them, the new ratio becomes 3:5. Find the numbers.
- a)7/2, 5/2
- b)3/2, 7/2
- c)9/2, 7/2
- d)11/2, 5/2
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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The ratio between two numbers is 7:5. If 5 is subtracted from each of ...
Answer – A.7/2, 5/2 Explanation : (7x – 5)/(5x – 5) = 3/5 X = 1/2 so the numbers are 7/2 and 5/2
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The ratio between two numbers is 7:5. If 5 is subtracted from each of ...
To solve this question, we can set up a system of equations using the given information.
Let's assume the two numbers are 7x and 5x, where x is a common factor. This assumption is based on the given ratio of 7:5.
According to the question, if we subtract 5 from each of the numbers, the new ratio becomes 3:5.
So, after subtracting 5 from each number, we have:
7x - 5 and 5x - 5
The new ratio is 3:5, which means:
(7x - 5)/(5x - 5) = 3/5
To solve this equation, we can cross-multiply:
5(7x - 5) = 3(5x - 5)
Expanding and simplifying:
35x - 25 = 15x - 15
Combine like terms:
35x - 15x = 25 - 15
20x = 10
Divide both sides by 20:
x = 10/20
Simplifying:
x = 1/2
Now that we have the value of x, we can substitute it back into the original assumption to find the numbers:
First number = 7x = 7(1/2) = 7/2
Second number = 5x = 5(1/2) = 5/2
Therefore, the two numbers are 7/2 and 5/2.
Hence, the correct answer is option A (7/2, 5/2).
Let's assume the two numbers are 7x and 5x, where x is a common factor. This assumption is based on the given ratio of 7:5.
According to the question, if we subtract 5 from each of the numbers, the new ratio becomes 3:5.
So, after subtracting 5 from each number, we have:
7x - 5 and 5x - 5
The new ratio is 3:5, which means:
(7x - 5)/(5x - 5) = 3/5
To solve this equation, we can cross-multiply:
5(7x - 5) = 3(5x - 5)
Expanding and simplifying:
35x - 25 = 15x - 15
Combine like terms:
35x - 15x = 25 - 15
20x = 10
Divide both sides by 20:
x = 10/20
Simplifying:
x = 1/2
Now that we have the value of x, we can substitute it back into the original assumption to find the numbers:
First number = 7x = 7(1/2) = 7/2
Second number = 5x = 5(1/2) = 5/2
Therefore, the two numbers are 7/2 and 5/2.
Hence, the correct answer is option A (7/2, 5/2).
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