Question

1. The present age of a man is five times the age of his son. Five years ago,
the age of the man was ten times the age of his son at that time. How old
is the man at present ?
(a) 45 years
(6) 48 years
(c) 49 years
(d) 52 years
(e) None of these​

Answer 1

Answer:-

• Father's age is 45 years and the sons age is 9 years.

To Find:-

• Find the present age of man.

Solution:-

According to Question:-

☯ Let the present age of son is " x " years.

Then the present age of man is "5x"

Five years ago,the age of the man was ten times the age of his son at that time.

• Five years ago the sons age is "x - 5"

• The father's age is " 5x - 5 "

️ ➭ 5x - 5 = 10 ( x - 5 )

️ ➭ 5x - 5 = 10x - 50

️ ➭ 10x - 5x = 50 - 5

️ ➭ 5x = 45

️ ➭ $\tt \boxed { \: x \: = \: 9 \: }$

Hence,

• Present age of son is x = 9.
• The present age of man is 5( 9 ) = 45 years.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

☯ Let Present age of son be x years.

Then, The Present age of Man will be 5x years.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

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

★Accordingtothequestion:

Five years ago, the age of the man was ten times the age of his son at that time.

⠀⠀⠀⠀

Their ages 5 years ago,

Age of Man = (5x - 5) years

Age of his son = (x - 5) years

⠀⠀⠀⠀

Therefore,

$\begin{gathered}:\implies\sf (5x - 5) = 10(x - 5)\\ \\ \\ :\implies\sf (5x - 5) = 10x - 50\\ \\ \\ :\implies\sf 5x - 10x = - 50 + 5\\ \\ \\ :\implies\sf - 5x = - 45\\ \\ \\ :\implies\sf x = \cancel{ \dfrac{-45}{-5}}\\ \\ \\ :\implies{\underline{\boxed{\frak{\purple{x = 9}}}}}\;\bigstar\\ \\\end{gathered}$

:⟹(5x−5)=10(x−5)

:⟹(5x−5)=10x−50

:⟹5x−10x=−50+5

:⟹−5x=−45

:⟹x=

−5

−45

:⟹

x=9

★

Hence,

Present age of son, x = 9 years

Present age of Man, 5x = 5 × 9 = 45 years

$\begin{gathered}\therefore\:{\underline{\sf{Present\:age\:of\:man\:is\: {\textsf{\textbf{45\:years}}}.}}}\\ \\\end{gathered}$

∴

Presentageofmanis45years.

$\bf{\dag}\:{\underline{\sf{Hence,\:Option\:(A)\:is\:correct.}}}$

Hence,Option(A)iscorrect.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\begin{gathered}\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\: Verification\:\bigstar}}}} \\ \\\end{gathered}$

★Verification★

Given that,

⠀⠀⠀⠀

Five years ago, the age of the man was ten times the age of his son.

⠀⠀⠀⠀

$\begin{gathered}:\implies\sf (45 - 5) = 10(9 - 5)\\ \\ \\ :\implies\sf 40 = 10 \times 4\\ \\ \\:\implies\sf 40 = 40\\ \\\end{gathered}$

:⟹(45−5)=10(9−5)

:⟹40=10×4

:⟹40=40

[tex]\qquad\qquad\qquad\quad\dag\:{\underline{\underline{\sf{\purple{Hence\: Verified!}}}}}[/tex