Question

Vivek is older than Kishore by 5 years the sum of the reciprocal of their age is 1/6 find their present age

Answer 1

Let their present ages be V and K, so we have

V = K + 5....(1)

1 / V + 1 / K = 1/6

K / VK + V / VK = 1/6

(V + K) / VK = 1/6

6(V + K) = VK

6V + 6K = VK....(2)

Solving (1) and (2), we get

6(K + 5) + 6K = (K + 5) K

6K +30 + 6K = K^2 + 5K

K^2 - 7K -30 = 0

K^2 -10K + 3K -30 = 0

K(K -10) + 3(K - 10) = 0

(K-10)(K +3) = 0

K = 10 or -3

K cant be -3, so 10 is our answer

Therefore Kishore is 10 yrs old, and Vivek is 15 yrs old

Answer 2

Hello Dear.

Here is the answer---

→→→→→→→→→

Let the present age of the Vivek and the Kishore be x and y years respectively.

In First Case,

Now, As per as the Questions,

 Vivek's age = 5 + Kishore's age
     x = 5 + y  ----eq(i)


In Second Case,

According to the Question,

 
 $\frac{1}{x} + \frac{1}{y} = \frac{1}{6}$

⇒ $\frac{x + y}{xy} = \frac{1}{6}$
⇒ 6(x + y) = xy
⇒ 6(5 + y + y) = (5 + y)y
⇒ 30 + 12y = 5y + y²
⇒ y² - 7y - 30 = 0
⇒ y² - 10y + 3y - 30 = 0
⇒ y(y - 10) + 3(y - 10) = 0
   (y + 3)(y - 10) = 0
⇒ y = -3  or  y = 10

∵ age cannot be negative, ∴ Rejecting y = -3.

∴ Kishore's age = y years
                          = 10 years.

Vivek's age = y + 5 years.
                   = 10 + 5
                   = 15 years


→→→→→→→→→


Hope it helps.

Have a Good Day.