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

☯ Let Present age of son be x years.

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

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

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

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Their ages 5 years ago,

• Age of Man = (5x - 5) years
• Age of his son = (x - 5) years

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Therefore,

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

Hence,

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

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

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

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

Given that,

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

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$:\implies\sf (45 - 5) = 10(9 - 5)\\ \\ \\ :\implies\sf 40 = 10 \times 4\\ \\ \\:\implies\sf 40 = 40$

$\qquad\qquad\qquad\quad\dag\:{\underline{\underline{\sf{\purple{Hence\: Verified!}}}}}$

Answer 2

Answer:

Given :-

• Man is 5 times of his son
• Five years ago the man was 10 times of son

To Find :-

Present age

Solution :-

Let the present age of son be x

And father age be 5x

$\tt \: x = 5x$

5 years age

$\tt \: x - 5 = 5x - 5$

$\tt \: 5x - 5 = 10(x - 5)$

$\tt \: 5x - 5 = 10x - 50$

$\tt \: 5x - 10x = 5 - 50$

$\tt \: - 5x = - 45$

$\tt \: x = \dfrac{ - 45}{ - 5}$

$\tt \: x \: = 9 \:$

Father age will be

$\tt \: 5x = 5(9) = 45$

Hence :-

$\huge \bf \odot \dag Option\: A$