Question

The sum of reciprocals of Rahul"s ages 3 years from now and 5 years ago is 1/3. What will be his age after 7 years

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Answer 1

Answer:

Rahul's Age after 7 years = 16 years

Step-by-step explanation:

Let Rahul's present age be x

Rahul's age after 3 years = 3 + x

Rahul's age 5 years ago = x - 5

According to the question :

$\frac{1}{3+x} + \frac{1}{x-5} = \frac{1}{3}$

⇒ $\frac{x-5 + 3+ x}{(3+x)(x-5)} = \frac{1}{3}$

⇒ $\frac{2x-2}{x^{2} -2x-15} = \frac{1}{3}$

⇒ $6x-6 = x^{2} -2x-15$

⇒ $x^{2} -8x - 9 = 0$

⇒ $x^{2} -9x+x-9=0$

⇒ $x(x-9)+(x-9) = 0$

⇒ $(x+1)(x-9)$

x = -1 , 9

∵ Age can't be negative.

Rahul's Present age = 9 years.

Rahul's Age after 7 years = 9 + 7 years

⇒ 16 years

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