Question

Ram's mother's present age is six times Ram's present age. five years from now, Ram's age will be 2/7th of his mother's age. what are their present ages?​

Answer 1

Answer:

Let,

The present ages of :-

• Ram be 'x'
• His mother be 'y'

According to question :-

1) Ram's mother's present age is six times Ram's present age

i.e

y = 6x

2) five years from now, Ram's age will be 2/7th of his mother's age.

x + 5 = (y + 5) $\sf\times\dfrac{2}{7}$

x + 5 = (6x + 5)$\sf\times\dfrac{2}{7}$

[Since, As y = 6x]

(x+5)$\sf\times 7 = (6x + 5)\times 2$

7x + 35 = 12x + 10

putting all constant terms to one side and all variable terms to another side :-

35 - 10 = 12x - 7x

25 = 5x

$x = \frac{25}{5}$

x = 5

$\sf\therefore$ Present age of Ram = x = 5years

Present age of his mother = y = 6x = 6(5) = 30years

Answer 2

$\large\textsf{ }$

$\LARGE\mathfrak{\underline\textcolor{aqua}{✯\; Solution :-}}$

$\large\textsf{ }$

• Let the present age of ram be ' x '
• Let the present age of his mother be ' y '

$\large\textsf{ }$

↦ According to the first condition :-

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf{y = 6x \; \; ------ ( i )}}$

$\large\textsf{ }$

↦ According to the second condition

$\large\textsf{ }$

$\qquad\tt{:}\longrightarrow\large\textsf{( x + 5 ) = \large \textsf{( y + 5 )} × \cfrac{\large\textsf{2}}{\large\textsf{7}} }$

$\qquad\tt{:}\longrightarrow\large\textsf{( x + 5 ) = \large \textsf{( 6x + 5 )} × \cfrac{\large\textsf{2}}{\large\textsf{7}} \; \; ------[ From ( i )]}$

$\qquad\tt{:}\longrightarrow\large\textsf{7 × ( x + 5 ) = ( 6x + 5 ) × 2}$

$\qquad\tt{:}\longrightarrow\large\textsf{7x + 35 = 12x + 10}$

$\qquad\tt{:}\longrightarrow\large\textsf{7x - 12x = 10 - 35}$

$\qquad\tt{:}\longrightarrow\large\textsf{- 5x = - 25}$

$\qquad\tt{:}\longrightarrow\large\textsf{ x = \cfrac{\large\textsf{- 25}}{\large\textsf{- 5}} }$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{x = 5}}$

$\large\textsf{ }$

↦ Substituting the value of x in ( i ) :-

$\qquad\tt{:}\longrightarrow\large\textsf{y = 6 × x}$

$\qquad\tt{:}\longrightarrow\large\textsf{y = 6 × 5}$

$\qquad\tt{:}\longrightarrow\boxed{\large\textsf\textcolor{red}{y = 30}}$

$\large\textsf{ }$

$\large\textsf\textcolor{orange}{∴ The present age of ram = 5 years}$

$\large\textsf\textcolor{orange}{∴ The present age of mother = 30 years}$

$\large\textsf{ }$

$\large\textsf\textcolor{purple}{ \; \; \; \; \; \; \; \; \; \; \; \; ◈ ━━━━━━━ ✪ ━━━━━━━ ◈}$