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The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age
Let the present age of Rehman be x years.
3 years ago, Rehman’s age was x - 3 years.
5 years from now, his age will be = x + 5
Using this information and the given condition, we can form the following quadratic equation:
1/(x - 3) + 1/(x + 5) = 1/3
[(x + 5) + (x - 3)] / (x - 3)(x + 5) = 1/3
(2x + 2) / x2 + 2x - 15 = 1/3
(2x + 2)(3) = x2 + 2x - 15
6x + 6 = x2 + 2x - 15
x2 + 2x - 15 = 6x + 6
x2 - 4x - 21 = 0
Let us now find the roots by factorization method:
x2 - 7x + 3x - 21 = 0
x(x - 7) + 3(x - 7) = 0
(x - 7) (x + 3) = 0
x - 7 = 0 and x + 3 = 0
x = 7 and x = - 3
But, age can’t be a negative value.
Therefore, Rehman’s present age is 7 years.
The sum of the reciprocals of Rehman’s age (in years) 3 years ago and 5 years from now is 1/3. Find his present age
Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.3 Question 4
The present age of Rehman is 7 years if the sum of the reciprocals of Rehman's age (in years) 3 years ago and 5 years from now is 1/3.
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