a two digit number is 3 more than 4 times the sum of its digits if 18 is added to the number its digits are reserved find the number​

Question

a two digit number is 3 more than 4 times the sum of its digits if 18 is added to the number its digits are reserved find the number​

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Emery 13 mins 2021-10-13T02:03:45+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-13T02:05:14+00:00

    SOLUTION :

    Let the ten’s digit number be r

    Let the one’s digit number be m

    \boxed{\bf{The\:original\:number\:=10r+m}}}}}\\\boxed{\bf{The\:reversed\:number\:=10m+r}}}}}

    A/q

    \longrightarrow\sf{10r+m=4(r+m)+3}\\\\\longrightarrow\sf{10r+m=4r+4m+3}\\\\\longrightarrow\sf{10r-4r+m-4m=3}\\\\\longrightarrow\sf{6r-3m=3}\\\\\longrightarrow\sf{6r=3+3m}\\\\\longrightarrow\sf{r=3+3m/6......................(1)}

    &

    \longrightarrow\sf{10r+m+18=10m+r}\\\\\longrightarrow\sf{10r-r+m-10m=-18}\\\\\longrightarrow\sf{9r-9m=-18}\\\\\longrightarrow\sf{9(r-m)=-18}\\\\\longrightarrow\sf{r-m=\cancel{-18/9}}\\\\\longrightarrow\sf{r-m=-2}\\\\\longrightarrow\sf{\dfrac{3+3m}{6} -m=-2\:\:\:\:[from(1)]}\\\\\longrightarrow\sf{3+3m-6m=-12}\\\\\longrightarrow\sf{3-3m=-12}\\\\\longrightarrow\sf{-3m=-12-3}\\\\\longrightarrow\sf{-3m=-15}\\\\\longrightarrow\sf{m=\cancel{-15/-3}}\\\\\longrightarrow\bf{m=5}

    ∴ Putting the value of m in equation (1),we get;

    \longrightarrow\sf{r=\dfrac{3+3(5)}{6} }\\\\\\\longrightarrow\sf{r=\dfrac{3+15}{6} }\\\\\\\longrightarrow\sf{r=\cancel{\dfrac{18}{6}} }\\\\\\\longrightarrow\bf{r=3}

    Thus;

    \underbrace{\sf{The\:number\:=10r+m=[10(3)+5]=[30+5]=\boxed{\bf{{35}}}}}}

    0
    2021-10-13T02:05:39+00:00

    Let the required number be ab.

    Sum of digits = a + b …….. ( 1 )

    10 a + b = 4 ( a + b )

    10 a + b + 18 = 10 b + a

    => 9 a + 18 = 9 b

    => a + 2 = b

    10 a + a + 2 = 4 ( a + a + 2 )

    => 11 a + 2 = 8 a + 8

    => 3 a = 6

    => a = 3

    => a + 2 = 5

    =>ab = 35……… [ A ]

    So the number becomes 35.

    ANSWER :

    The original number is 35.

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