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The sum of two positive numebrs is 100. After subtracting 5 from each number, the product of the resulting numbers is 0. One of the original numbers is ______.
- a)95
- b)90
- c)85
- d)80
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The sum of two positive numebrs is 100. After subtracting 5 from each ...
If the product of two positive numbers should be zero, one of the number must be zero.
After subtracting 5 if a positive number should become zero, that number should be 5.
If one number is 5 and the sum is 100 then the other number must be 95.
Let the two positive numbers be x and y.
∴ x + y = 100 ...(i)
(x – 5) (y – 5) = 0 ...(ii)
⇒ x = 5 or y = 5
If x = 5 then y = 95
If y = 5 then x = 95
∴ One of the number is 95 since 5 is not in any of the options.
After subtracting 5 if a positive number should become zero, that number should be 5.
If one number is 5 and the sum is 100 then the other number must be 95.
Let the two positive numbers be x and y.
∴ x + y = 100 ...(i)
(x – 5) (y – 5) = 0 ...(ii)
⇒ x = 5 or y = 5
If x = 5 then y = 95
If y = 5 then x = 95
∴ One of the number is 95 since 5 is not in any of the options.
Most Upvoted Answer
The sum of two positive numebrs is 100. After subtracting 5 from each ...
Solution:
Let the two positive numbers be x and y.
Given, x + y = 100
Subtracting 5 from each number, we get (x-5) and (y-5).
Given, (x-5) * (y-5) = 0
To get a product of 0, either (x-5) or (y-5) should be zero.
Case 1: (x-5) = 0
Adding 5 to both sides, we get x = 5
But x should be a positive number, so this case is not possible.
Case 2: (y-5) = 0
Adding 5 to both sides, we get y = 5
But y should be a positive number, so this case is not possible.
Case 3: (x-5) * (y-5) = 0 can be written as x*y - 5x - 5y + 25 = 0
Substituting x + y = 100, we get:
x*y - 5x - 5y + 25 = 0
x*y - 5x - 5(100-x) + 25 = 0
x*y - 5x - 500 + 5x + 25 = 0
x*y - 475 = 0
x*y = 475
Now, we need to find the values of x and y such that x + y = 100 and x*y = 475
By trial and error, we can find that x = 95 and y = 5 satisfy these conditions.
Therefore, one of the original numbers is 95.
Hence, the correct option is (A) 95.
Let the two positive numbers be x and y.
Given, x + y = 100
Subtracting 5 from each number, we get (x-5) and (y-5).
Given, (x-5) * (y-5) = 0
To get a product of 0, either (x-5) or (y-5) should be zero.
Case 1: (x-5) = 0
Adding 5 to both sides, we get x = 5
But x should be a positive number, so this case is not possible.
Case 2: (y-5) = 0
Adding 5 to both sides, we get y = 5
But y should be a positive number, so this case is not possible.
Case 3: (x-5) * (y-5) = 0 can be written as x*y - 5x - 5y + 25 = 0
Substituting x + y = 100, we get:
x*y - 5x - 5y + 25 = 0
x*y - 5x - 5(100-x) + 25 = 0
x*y - 5x - 500 + 5x + 25 = 0
x*y - 475 = 0
x*y = 475
Now, we need to find the values of x and y such that x + y = 100 and x*y = 475
By trial and error, we can find that x = 95 and y = 5 satisfy these conditions.
Therefore, one of the original numbers is 95.
Hence, the correct option is (A) 95.
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Community Answer
The sum of two positive numebrs is 100. After subtracting 5 from each ...
Let the numbers be x,y
x + y =100
and (x-5)(y-5)=0 that means x =5 or y=5
i.e one of the numbers is 5 so the other number must be 95
x + y =100
and (x-5)(y-5)=0 that means x =5 or y=5
i.e one of the numbers is 5 so the other number must be 95
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The sum of two positive numebrs is 100. After subtracting 5 from each number, the product of the resulting numbers is 0. One of the original numbers is ______.a)95b)90c)85d)80Correct answer is option 'A'. Can you explain this answer?
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