# Quadratic Equations | Word Problem

Exercise 4.3 Q4. CBSE 10th Maths NCERT exercise solution

#### Question: The sum of the reciprocals of Rehman’s ages (in years) 3 years ago and 5 years from now is $$frac{1}{3}$. Find his present age. #### Video Explanation #### Explanatory Answer Let the present age of Rehman be x. 3 years ago his age would have been$x - 3).
5 years from now his age would be (x + 5).

Given: Sum of reciprocals of age 3 years ago and 5 years from now is $$frac{1}{3}$ Age 3 years ago was$x - 3). So, reciprocal of age 3 years ago = $$frac{1}{x - 3}$ ----------------$1)
Age 5 years from now is (x + 5). So, reciprocal of age 5 years from now = $$frac{1}{x + 5}$ ----------------$2)
Sum of (1) and (2) = $$frac{1}{x - 3}$ + $\frac{1}{x + 5}$ = $\frac{1}{3}$ Because x cannot be 3 or -5 multiply the equation by$x - 3) (x + 5)
(x + 5) + (x – 3) = $$frac{1}{3}$$x - 3) (x + 5)
2x + 2 = $$frac{1}{3}$$x – 3) (x + 5)
Multiply the equation by 3
3(2x + 2) = (x – 3) (x + 5)
6x + 6 = x2 + 5x - 3x - 15
x2 - 4x - 21 = 0

##### Find the values of x by factorizing the quadratic equation

x2 - 7x + 3x - 21 = 0
x(x – 7) + 3(x – 7) = 0
(x – 7) (x + 3) = 0
x = 7 and x = -3
x is the present age of Rehman. Present age cannot be negative.
Hence, Rehman’s present age is 7 years.