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There are two consecutive numbers such that the difference of their reciprocals is 1/240. The numbers are
- a)15,16
- b)17, 18
- c)13, 14
- d)12, 13
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
There are two consecutive numbers such that the difference of their re...
**Given Information:**
- There are two consecutive numbers.
- The difference of their reciprocals is 1/240.
**Let's assume the two consecutive numbers:**
- Let the first number be x.
- The next consecutive number will be x + 1.
**Reciprocal of a number:**
- The reciprocal of a number n is denoted as 1/n.
**Given condition:**
- The difference of the reciprocals of the two numbers is 1/240.
- Mathematically, it can be represented as:
(1/x) - (1/(x + 1)) = 1/240
**Solving the equation:**
- To solve the equation, we can cross-multiply to get rid of the denominators:
(x + 1) - x = (1/240) * x * (x + 1)
- Simplifying the equation:
1 = (1/240) * (x^2 + x)
- Multiplying both sides by 240 to eliminate the fraction:
240 = x^2 + x
- Rearranging the equation:
x^2 + x - 240 = 0
- Factoring the quadratic equation:
(x - 15)(x + 16) = 0
- Setting each factor equal to zero and solving for x:
x - 15 = 0 OR x + 16 = 0
x = 15 OR x = -16
Since the problem states that the numbers are consecutive, we can discard the negative value for x. Therefore, the first number is 15.
**Finding the second number:**
- The second number is the next consecutive number after 15, which is 15 + 1 = 16.
Hence, the two consecutive numbers that satisfy the given condition are 15 and 16, which corresponds to option A.
- There are two consecutive numbers.
- The difference of their reciprocals is 1/240.
**Let's assume the two consecutive numbers:**
- Let the first number be x.
- The next consecutive number will be x + 1.
**Reciprocal of a number:**
- The reciprocal of a number n is denoted as 1/n.
**Given condition:**
- The difference of the reciprocals of the two numbers is 1/240.
- Mathematically, it can be represented as:
(1/x) - (1/(x + 1)) = 1/240
**Solving the equation:**
- To solve the equation, we can cross-multiply to get rid of the denominators:
(x + 1) - x = (1/240) * x * (x + 1)
- Simplifying the equation:
1 = (1/240) * (x^2 + x)
- Multiplying both sides by 240 to eliminate the fraction:
240 = x^2 + x
- Rearranging the equation:
x^2 + x - 240 = 0
- Factoring the quadratic equation:
(x - 15)(x + 16) = 0
- Setting each factor equal to zero and solving for x:
x - 15 = 0 OR x + 16 = 0
x = 15 OR x = -16
Since the problem states that the numbers are consecutive, we can discard the negative value for x. Therefore, the first number is 15.
**Finding the second number:**
- The second number is the next consecutive number after 15, which is 15 + 1 = 16.
Hence, the two consecutive numbers that satisfy the given condition are 15 and 16, which corresponds to option A.
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There are two consecutive numbers such that the difference of their reciprocals is 1/240. The numbers area)15,16b)17, 18c)13, 14d)12, 13Correct answer is option 'A'. Can you explain this answer?
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