Question

The difference between present ages of Ram and Gaurav is 10 years. After 5 years, Ram's
is 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.

⠀

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.

⠀

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

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

$:\implies\sf x - y = 10$

$:\implies\sf x = 10 + y\qquad\qquad\bigg\lgroup\bf eq\;(1) \bigg\rgroup$

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

⠀

Their ages after 5 years,

⠀

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

⠀

Therefore,

⠀

$:\implies\sf (x + 5) = 2(y + 5)$

$:\implies\sf x + 5 = 2y + 10$

$:\implies\sf (10 + y) + 5 = 2y + 10$

$:\implies\sf 15 + y = 2y + 10$

$:\implies\sf y - 2y = 10 - 15$

$:\implies\sf - y = - 5$

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

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

⠀

$:\implies\sf x = 10 + 5$

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

Therefore,

⠀

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

Answer 2

Given :-

• Difference between age ram and gaurav = 10
• After 5 years, Ram's is twice of Gaurav's age.

To find :-

Present age of Ram

SoluTion :-

☯ Let present age of Ram be x and gaurav be y.

Therefore,

➞ x - y = 10

➞ x = 10 + y ❬Eq 1❭

• After 5 years

➞ (x + 5) = 2(y + 5)

➞ (x + 5) = 2y + 10

➞ (10 + y) + 5 = 2y + 10

➞ 15 + y = 2y + 10

➞ y - 2y = 10 - 15

➞ -y = -5

Age can't be negative

Therefore,

$\huge \bf \: Y \: = 5$

Now, Putting value of y in eq (1)

➞ x = 10 + y

➞ x = 10 + 5

➞ x = 15 year

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