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The question is written in Hindi, and it states:

**"रहमान की 3 वर्ष पूर्व व 5 वर्ष बाद की आयु के व्युक्तम का योग 1/3 हो तो रहमान की वर्तमान आयु है—"**

Translation:

**"The sum of the reciprocals of Rahman's age 3 years ago and 5 years from now is 1/3. What is Rahman's current age?"**

Let Rahman's current age be \( x \) years.

- 3 years ago, Rahman's age was \( x - 3 \).
- 5 years from now, Rahman's age will be \( x + 5 \).

The sum of the reciprocals of these two ages is given as:

\[
\frac{1}{x - 3} + \frac{1}{x + 5} = \frac{1}{3}
\]

Now, let's solve this equation step by step:

\[
\frac{1}{x - 3} + \frac{1}{x + 5} = \frac{1}{3}
\]

Take the LCM of \( x - 3 \) and \( x + 5 \):

\[
\frac{(x + 5) + (x - 3)}{(x - 3)(x + 5)} = \frac{1}{3}
\]

Simplify the numerator:

\[
\frac{2x + 2}{(x - 3)(x + 5)} = \frac{1}{3}
\]

Now cross-multiply:

\[
3(2x + 2) = (x - 3)(x + 5)
\]

Expand both sides:

\[
6x + 6 = x^2 + 5x - 3x - 15
\]

\[
6x + 6 = x^2 + 2x - 15
\]

Rearrange the terms:

\[
x^2 + 2x - 6x - 15 - 6 = 0
\]

\[
x^2 - 4x - 21 = 0
\]

Now solve this quadratic equation using the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-21)}}{2(1)}
\]

\[
x = \frac{4 \pm \sqrt{16 + 84}}{2}
\]

\[
x = \frac{4 \pm \sqrt{100}}{2}
\]

\[
x = \frac{4 \pm 10}{2}
\]

So, \( x = \frac{4 + 10}{2} = 7 \) or \( x = \frac{4 - 10}{2} = -3 \).

Since age cannot be negative, Rahman's current age is \( \boxed{7} \).

The correct answer is **Option A: 7**.

---

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How can you solve a similar problem with different years?
2. How does the reciprocal equation work in different scenarios?
3. What is the importance of the quadratic formula in such age problems?
4. Can we solve this problem using trial and error instead of algebraic methods?
5. How do we apply this method to other real-life scenarios involving age?

**Tip:** Always check the feasibility of your solution when dealing with real-world problems like age. Negative answers typically aren't valid for such contexts.

रहमान की 3 वर्ष पूर्व व 5 वर्ष बाद की आयु के व्युक्तम का योग 1/3 हो तो रहमान की वर्तमान आयु है—

Learn how to solve for Rahman's age by using the sum of reciprocals of ages 3 years ago and 5 years later. The problem is solved using reciprocal and quadratic equations. Suitable for students in Grades 7-9.

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