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There are two consecutive numbers such that the difference of their reciprocal is 1/240?
Most Upvoted Answer
There are two consecutive numbers such that the difference of their re...
Introduction:
The problem requires finding two consecutive numbers whose reciprocal difference equals 1/240. This can be solved algebraically using a system of equations.
Solution:
Let x be the first number, then the second number is x+1. The reciprocal of x is 1/x and the reciprocal of x+1 is 1/(x+1).
We can set up the equation:
1/x - 1/(x+1) = 1/240
Simplifying the equation:
Multiplying both sides by x(x+1) gives us:
(x+1) - x = x(x+1)/240
Simplifying the left side:
1 = x(x+1)/240
Multiplying both sides by 240:
240 = x(x+1)
Using the quadratic formula:
Rearranging the equation to standard quadratic form gives:
x^2 + x - 240 = 0
Using the quadratic formula:
x = (-1 ± sqrt(1 + 4(240)))/2
x = (-1 ± 49)/2
We can discard the negative root:
x = 24
Therefore, the two consecutive numbers are 24 and 25.
Conclusion:
The solution shows that the two consecutive numbers that satisfy the condition are 24 and 25. This problem can be solved using basic algebraic manipulation and the quadratic formula.
The problem requires finding two consecutive numbers whose reciprocal difference equals 1/240. This can be solved algebraically using a system of equations.
Solution:
Let x be the first number, then the second number is x+1. The reciprocal of x is 1/x and the reciprocal of x+1 is 1/(x+1).
We can set up the equation:
1/x - 1/(x+1) = 1/240
Simplifying the equation:
Multiplying both sides by x(x+1) gives us:
(x+1) - x = x(x+1)/240
Simplifying the left side:
1 = x(x+1)/240
Multiplying both sides by 240:
240 = x(x+1)
Using the quadratic formula:
Rearranging the equation to standard quadratic form gives:
x^2 + x - 240 = 0
Using the quadratic formula:
x = (-1 ± sqrt(1 + 4(240)))/2
x = (-1 ± 49)/2
We can discard the negative root:
x = 24
Therefore, the two consecutive numbers are 24 and 25.
Conclusion:
The solution shows that the two consecutive numbers that satisfy the condition are 24 and 25. This problem can be solved using basic algebraic manipulation and the quadratic formula.
Community Answer
There are two consecutive numbers such that the difference of their re...
1/x -1/y=1/240.
y - x=1(they are consecutive numbers)
(y - x)/y x = 1/240
240(y - x) =y x ( y - x =1)
240 = x y
also y - x=1 ;y =1+x
240 = x (1+x)
240= 15×16
hence,the numbers are 15 and 16.
y - x=1(they are consecutive numbers)
(y - x)/y x = 1/240
240(y - x) =y x ( y - x =1)
240 = x y
also y - x=1 ;y =1+x
240 = x (1+x)
240= 15×16
hence,the numbers are 15 and 16.
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There are two consecutive numbers such that the difference of their reciprocal is 1/240?
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There are two consecutive numbers such that the difference of their reciprocal is 1/240? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are two consecutive numbers such that the difference of their reciprocal is 1/240? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two consecutive numbers such that the difference of their reciprocal is 1/240?.
There are two consecutive numbers such that the difference of their reciprocal is 1/240? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about There are two consecutive numbers such that the difference of their reciprocal is 1/240? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two consecutive numbers such that the difference of their reciprocal is 1/240?.
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