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The product of two positive numbers is 2500. If one number is four times the other, then what will be the sum of the two numbers?
- a)25
- b)125
- c)225
- d)250
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The product of two positive numbers is 2500. If one number is four tim...
Let the two numbers be x and y.
Given,
xy = 2500
And x is four times y.
⇒ x = 4y ----(1)
Putting the value of x in (1), we get
⇒ 4y2 = 2500
⇒ y2 = 625
⇒ y = 25
The numbers are x = 4 × y = 100 and y = 25
Sum of two numbers = 100 + 25 = 125
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The product of two positive numbers is 2500. If one number is four tim...
Given information:
- The product of two positive numbers is 2500.
- One number is four times the other.
Let's assume the two positive numbers as 'x' and 'y'.
From the given information, we can form the following equations:
Equation 1: x * y = 2500
Equation 2: x = 4y
To find the sum of the two numbers, we need to determine the values of 'x' and 'y'.
Substituting Equation 2 into Equation 1, we get:
(4y) * y = 2500
4y^2 = 2500
Now, let's solve this quadratic equation to find the value of 'y':
4y^2 = 2500
Dividing both sides by 4:
y^2 = 625
Taking the square root of both sides:
y = ±√625
y = ±25
Since we are given that the numbers are positive, we take the positive value:
y = 25
Substituting this value into Equation 2, we can find the value of 'x':
x = 4 * 25
x = 100
The two numbers are 100 and 25.
Now, let's calculate the sum of the two numbers:
Sum = x + y
Sum = 100 + 25
Sum = 125
Therefore, the sum of the two numbers is 125, which matches option B.
- The product of two positive numbers is 2500.
- One number is four times the other.
Let's assume the two positive numbers as 'x' and 'y'.
From the given information, we can form the following equations:
Equation 1: x * y = 2500
Equation 2: x = 4y
To find the sum of the two numbers, we need to determine the values of 'x' and 'y'.
Substituting Equation 2 into Equation 1, we get:
(4y) * y = 2500
4y^2 = 2500
Now, let's solve this quadratic equation to find the value of 'y':
4y^2 = 2500
Dividing both sides by 4:
y^2 = 625
Taking the square root of both sides:
y = ±√625
y = ±25
Since we are given that the numbers are positive, we take the positive value:
y = 25
Substituting this value into Equation 2, we can find the value of 'x':
x = 4 * 25
x = 100
The two numbers are 100 and 25.
Now, let's calculate the sum of the two numbers:
Sum = x + y
Sum = 100 + 25
Sum = 125
Therefore, the sum of the two numbers is 125, which matches option B.
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The product of two positive numbers is 2500. If one number is four times the other, then what will be the sum of the two numbers?a)25b)125c)225d)250Correct answer is option 'B'. Can you explain this answer?
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