Question

The difference between present ages of Ram and Gaurav is 12 years. After 5 years, Ram's age will be twice of Gaurav's age. The present age (in years) of Ram is​

Answer 1

Step-by-step explanation:

Given :-

The difference between present ages of Ram and Gaurav is 10 years.

After 5 years, Ram's is twice of Gaurav's age.

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To Find :-

Present age of Ram?

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☯ Let's Consider the present age of Ram and Gaurav be x and y years respectively.

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\begin{gathered}\begin{gathered}\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\\end{gathered} \end{gathered}

★Accordingtothequestion:

The difference between present ages of Ram and Gaurav is 10 years.

\begin{gathered}\begin{gathered}:\implies\sf x - y = 10\\ \\\end{gathered} \end{gathered}

:⟹x−y=10

\begin{gathered}\begin{gathered}:\implies\sf x = 10 + y\qquad\qquad\bigg\lgroup\bf eq\;(1) \bigg\rgroup\\ \\\end{gathered} \end{gathered}

:⟹x=10+y

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eq(1)

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After 5 years, Ram's is twice of Gaurav's age.

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Their ages after 5 years,

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Age of Ram = (x + 5) years

Age of Gaurav = (y + 5) years

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Therefore,

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\begin{gathered}\begin{gathered}:\implies\sf (x + 5) = 2(y + 5)\\ \\\end{gathered} \end{gathered}

:⟹(x+5)=2(y+5)

\begin{gathered} < /p > < p > \begin{gathered}:\implies\sf x + 5 = 2y + 10\\ \\\end{gathered} \end{gathered}

</p><p>

:⟹x+5=2y+10

\begin{gathered}\begin{gathered}:\implies\sf (10 + y) + 5 = 2y + 10\\ \\\end{gathered} \end{gathered}

:⟹(10+y)+5=2y+10

\begin{gathered}\begin{gathered}:\implies\sf 15 + y = 2y + 10\\ \\\end{gathered} \end{gathered}

:⟹15+y=2y+10

\begin{gathered}\begin{gathered}:\implies\sf y - 2y = 10 - 15\\ \\\end{gathered} \end{gathered}

:⟹y−2y=10−15

\begin{gathered}\begin{gathered}:\implies\sf - y = - 5\\ \\\end{gathered} \end{gathered}

:⟹−y=−5

\begin{gathered} < /p > < p > \begin{gathered}:\implies{\underline{\boxed{\sf{\purple{y = 5}}}}}\;\bigstar\\ \\\end{gathered} \end{gathered}

</p><p>

:⟹

y=5

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Now, Putting value of y in eq (1),

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\begin{gathered}\begin{gathered}:\implies\sf x = 10 + 5\\ \\\end{gathered} < /p > < p > \end{gathered}

:⟹x=10+5

</p><p>

\begin{gathered}\begin{gathered}:\implies{\underline{\boxed{\sf{\pink{x = 15}}}}}\;\bigstar\\ \\\end{gathered} \end{gathered}

:⟹

x=15

★

Therefore,

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Present age of Ram, x = 15 years

Present age of Gaurav, y = 5 years