Question

The difference between present ages of Ram and Gaurav is 10 years. After 5 years, Ram's age will be twice of Gaurav's age. The present age (in years) of Ram is​

Answer 1

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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Solution:

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

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According to the question:-

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

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

$\begin{gathered}:\implies\sf x = 10 + y --(1)\\ \\\end{gathered}$

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

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Their ages after 5 years

• Age of Ram = (x + 5) years
• Age of Gaurav = (y + 5) years

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Therefore,

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

$\begin{gathered}:\implies\sf x + 5 = 2y + 10\\ \\\end{gathered}$

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

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

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

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

$\begin{gathered}:\implies{\underline{\boxed{\sf{\purple{y = 5}}}}}\;\bigstar\\ \\\end{gathered}$

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$\; \; \; \; \; \; \; \sf{\underline{\orange{Now,\; Putting \;value\; of\; y \;in \;eq\; (1),}}}$

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$\begin{gathered}:\implies\sf x = 10 + 5\\ \\\end{gathered}$

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

Therefore,

• Present age of Ram, x = 15 years
• Present age of Gaurav, y = 5 years

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Answer 2

Given

• The difference between present ages of Ram and Gaurav is 10 years.
• After 5 years, Ram's age will be twice of Gaurav's age.

⠀

To find

• Present age of Ram.

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Solution

• Let the present age of Ram be x.
• Let the present age of Gaurav be y.

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$\: \: \: \: \: \: \: \: \: \:\small{\underline{\sf{\red{Difference\: between\: their\: ages\: is\: 10\: years}}}}$

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$\tt\longrightarrow{x - y = 10}$⠀⠀...[1]

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★⠀After 5 years⠀★

• Ram's age = x + 5
• Gaurav's age = y + 5

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$\: \: \: \: \: \: \: \: \: \: \small{\underline{\sf{\red{Ram's\: age\: will\: be\: twice\: of\: Gaurav's\: age}}}}$

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$\tt\longrightarrow{(x + 5) = 2(y + 5)}$

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$\tt\longrightarrow{x + 5 = 2y + 10}$

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$\tt\longrightarrow{x - 2y = 5}$⠀⠀ ....[2]

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\orange{Subtracting\: [2]\: from\: [1]}}}$

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$\tt:\implies{(x - y) - (x - 2y) = 10 - 5}$

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$\tt:\implies{\cancel{x} - y - \cancel{x} + 2y = 5}$

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$\tt:\implies{-y + 2y = 5}$

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$\bf:\implies{y = 5}$

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\orange{Putting\: the\: value\: of\: x\: in\: [1]}}}$

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$\tt:\implies{x - 5 = 10}$

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$\bf:\implies{x = 15}$

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Hence,

• Present age of Ram is 15 years.
• Present age of Gaurav is 5 years.

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