Question

विवेक, हा किशोरपेक्षा 5 वर्षांनी मोठा असून त्यांच्या वयांच्या गुणाकार व्यस्तांची बेरीज $\frac{1}{6}$ आहे, तर त्यांची आजची वये काढा.

Answer 1

Given:

विवेक, हा किशोरपेक्षा 5 वर्षांनी मोठा असून त्यांच्या वयांच्या गुणाकार व्यस्तांची बेरीज  1/6 आहे,

Vivek is older than Kishor by 5years. The sum of the reciprocals of their ages is 1/6.

To find:

तर त्यांची आजची वये काढा.

Their present ages

Solution:

Vivek is older than Kishor by 5 years

Let,

"x" years → be Kishore's present age

"( x + 5 )" years → be Vivek's present age

As per the question, we can form an equation as,

The sum of reciprocals = $\frac{1}{6}$

i.e., $\frac{1}{x} + \frac{1}{(x + 5)} = \frac{1}{6}$

$\implies \frac{x+ 5 + x}{x (x + 5)} = \frac{1}{6}$

$\implies \frac{2x+ 5 }{x^2 + 5x} = \frac{1}{6}$

$\implies 6( 2x + 5 ) = x(x + 5 )$

$\implies 12x + 30 = x^2 + 5x$

$\implies x^2 + 5x - 12x - 30 = 0$

$\implies x^2 - 7x - 30 = 0$

$\implies x^2 - 10x + 3x - 30 = 0$

$\implies x( x - 10 ) + 3(x - 10 ) = 0$

$\implies ( x - 10 )( x + 3 ) = 0$

$\implies x = 10 \:or\: -3$

since age cannot be negative

∴ $\bold{x = 10 \:years}$ ← Kishor's age

and

∴ $x + 5 = 10 + 5 = \bold{15}$ ← Vivek's age

Thus,

$\boxed{\bold{Vivek's \:present \:age\rightarrow\underline{15\:years}}}\\\\\boxed{\bold{Kishor's \:present \:age\rightarrow\underline{10\:years}}}$

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