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The difference between two numbers is 22 and their product is 240, what is the difference between their reciprocals ?
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The difference between two numbers is 22 and their product is 240, wha...
Understanding the Problem
To solve the problem, we need to establish two numbers based on the given conditions: their difference is 22, and their product is 240. Let’s denote the two numbers as x and y.
Step 1: Forming Equations
- From the difference:
x - y = 22 (Equation 1)
- From the product:
x * y = 240 (Equation 2)
Step 2: Expressing One Variable
From Equation 1, we can express x in terms of y:
x = y + 22
Step 3: Substituting in the Product Equation
Substituting x in Equation 2:
(y + 22) * y = 240
This simplifies to:
y^2 + 22y - 240 = 0
Step 4: Solving the Quadratic Equation
Now, we can solve this quadratic equation using the quadratic formula or factoring. The factors of -240 that add up to 22 are 30 and -8. Thus, we can factor the equation as:
(y + 30)(y - 8) = 0
This gives us:
y = -30 or y = 8
Since y represents a number, we take y = 8. Then from Equation 1, x = 8 + 22 = 30.
Step 5: Finding the Reciprocals
Now, we can find the difference between their reciprocals:
1/x - 1/y = (y - x) / (xy)
Substituting x and y:
1/30 - 1/8 = (8 - 30) / (240)
Final Calculation
This simplifies to:
-22 / 240 = -11 / 120
Thus, the difference between the reciprocals of the two numbers is -11/120.
To solve the problem, we need to establish two numbers based on the given conditions: their difference is 22, and their product is 240. Let’s denote the two numbers as x and y.
Step 1: Forming Equations
- From the difference:
x - y = 22 (Equation 1)
- From the product:
x * y = 240 (Equation 2)
Step 2: Expressing One Variable
From Equation 1, we can express x in terms of y:
x = y + 22
Step 3: Substituting in the Product Equation
Substituting x in Equation 2:
(y + 22) * y = 240
This simplifies to:
y^2 + 22y - 240 = 0
Step 4: Solving the Quadratic Equation
Now, we can solve this quadratic equation using the quadratic formula or factoring. The factors of -240 that add up to 22 are 30 and -8. Thus, we can factor the equation as:
(y + 30)(y - 8) = 0
This gives us:
y = -30 or y = 8
Since y represents a number, we take y = 8. Then from Equation 1, x = 8 + 22 = 30.
Step 5: Finding the Reciprocals
Now, we can find the difference between their reciprocals:
1/x - 1/y = (y - x) / (xy)
Substituting x and y:
1/30 - 1/8 = (8 - 30) / (240)
Final Calculation
This simplifies to:
-22 / 240 = -11 / 120
Thus, the difference between the reciprocals of the two numbers is -11/120.
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The difference between two numbers is 22 and their product is 240, what is the difference between their reciprocals ?
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The difference between two numbers is 22 and their product is 240, what is the difference between their reciprocals ? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference between two numbers is 22 and their product is 240, what is the difference between their reciprocals ? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between two numbers is 22 and their product is 240, what is the difference between their reciprocals ?.
The difference between two numbers is 22 and their product is 240, what is the difference between their reciprocals ? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The difference between two numbers is 22 and their product is 240, what is the difference between their reciprocals ? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference between two numbers is 22 and their product is 240, what is the difference between their reciprocals ?.
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