The sum of the age of a man and his son is 45 years.five years ago,the product of their age was four times the man’s age at that time.find t

Question

The sum of the age of a man and his son is 45 years.five years ago,the product of their age was four times the man’s age at that time.find their present age

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Audrey 2 months 2021-10-04T21:14:26+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-04T21:16:10+00:00

    Answer:

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    Step-by-step explanation:

    Ans : 36 years, 9 years

    Hint :

    Let the present age of the man be x years. Then, present age of his son is (45 – x) years. Five years ago, man’s age = (x – 5) years. Son’s age = (45 – x – 5) years.

    ∴ (x – 5) (45 – x – 5) = 4(x – 5)

    0
    2021-10-04T21:16:18+00:00

    Solution :

    Let the present age of a man be r years & let the present age of son be m years respectively;

    \underline{\underline{\tt{According\:to\:the\:question\::}}}

    \underbrace{\bf{1^{st} \:Case\::}}

    \mapsto\tt{r+m=45}

    \mapsto\tt{m=45-r...................(1)}

    \underbrace{\bf{2^{nd} \:Case\::}}

    \underbrace{\bf{5\:years\:ago\::}}

    The age of man’s was = (r – 5) years .

    The age of son’s was = (m – 5) years .

    Now;

    \mapsto\tt{(r-5) (m-5) = 4(r-5)}

    \mapsto\tt{(r-5) (45-r-5) = 4(r-5)\:\:\:[from(1)]}

    \mapsto\tt{(r-5) (40-r) = 4(r-5)}

    \mapsto\tt{r(40-r) -5(40-r) = 4r - 20}

    \mapsto\tt{40r-r^{2} -200 +5r  = 4r - 20}

    \mapsto\tt{45r-r^{2} -200 +20 -4r =0}

    \mapsto\tt{41r -r^{2} -180 = 0}

    \mapsto\tt{r^{2}  -41r +180 = 0}

    \mapsto\tt{r^{2}  -36r - 5r +180 = 0}

    \mapsto\tt{r(r-36)  -5(r-36)  = 0}

    \mapsto\tt{(r-36) (r-5) = 0}

    \mapsto\tt{r-36 =0\:\:\:Or\:\:\:r-5=0}

    \mapsto\bf{r=36\:\:\:Or\:\:\:r\neq 5}

    As we know that never may 5 years the age of man, so not acceptable .

    ∴ Putting the value of r = 36 in equation (1),we get;

    \mapsto\tt{m=45-36}

    \mapsto\bf{m=9\:years}

    Thus;

    The present age of man’s = r = 36 years .

    The present age of son’s = m = 9 years .

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