Question

Sum of the reciprocals of man's age(in years) 5years ago and 4 years from now is 29/190. Find s present age.

Answer 1

Let the man's age be A
His age 5 years ago will be A - 5
His age 4 years from now will be A + 4

[ 1 / (A - 5) ] + [ 1 / (A + 4) ] = 29 / 190
[ (A + 4) + (A - 5) ] / [ (A - 5)x(A + 4) ] = 29 / 190
(2A - 1) / (A² + 4A - 5A - 20) = 29 / 190
190 x (2A - 1) = 29 x (A² + 4A - 5A - 20)
380A - 190 = 29 x (A² - A - 20)
380A - 190 = 29A² - 29A - 580
380A + 29A - 190 + 580 = 29A²
409A + 390 = 29A²
29A² - 409A - 390 = 0

By solving equation ,
A = 15 years