the sum of the reciprocal of rehmans ages(in years) 3 years ago and 5 years from now is 1/3 find his present age.
please tell me from which chapter the following question is and also its solution.
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Answer:
7 years
Step-by-step explanation:
Let the present age of rehman be x.
Age 3 years ago = x -3 .
Age 5 years from now = x + 5.
given, Sum of reciprocal of these ages is 1/3.
=> 1/x -3 + 1/x +5 = 1/3
=> x + 5 + x -3 /(x+5)(x-3) = 1/3
=> 2x +2 / x² +2x - 15 = 1/3
=> 6x +6 = x² +2x - 15
=> x² - 4x - 21 = 0
=> x² - 7x + 3x - 21 = 0
=> x(x-7) + 3(x-7) = 0
=> (x-7)(x+3)= 0
=> x = 7 or -3.
Since age cannot be negative x = -3 can be discarded.
Thus the age of rehman = 7 yrs.
This would be belong to chapter "Quadratic equations" Chapter 4, NCERT class 10th
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