Question

18. Sum of the reciprocals of a man's age (in years) 5 years ago and 4 years from now is29/190
Find his present age.​

Answer 1

Answer:

15 years.

Explanation:

Let the man’s age be x

According to the question his age 5 years ago will be x – 5

Also his age 4 years from now will be x + 4

Now 1/x – 5 + 1 / x + 4 = 29 / 190

So x + 4 + x – 5 / (x – 5) (x + 4) = 29 / 190

2 x – 1 / x^2 – 5x + 4x – 20 = 29 / 190

2x – 1 / x^2 – x – 20 = 29 / 190

380 x – 190 = 29 x^2 – 29 x – 580

380 x + 29 x – 29 x^2 – 190 + 580 = 0

29 x^2 – 409 x – 390 = 0

Now x = - b ± √b^2 – 4ac / 2a

        x = - (- 409) ± √(409)^2 – 4(29)(- 390) / 2 (29)

         x = 409 ± √212521 / 58

         x = 409 + 461 / 58

         x = 870 / 58

         x = 15 years.

So his present age is 15 years.