Question

I shall write a two digit number,the sum of two digits of which is 14 and if 29 is substracted from the number,the two digits will be equal.Let us form the simultaneous equation by solving them and let us see what will be the 2 digit number

Answer 1

the two digit no is 95

Answer 2

$\huge\ \sf{\red {[[«\: คꈤ \mathfrak Sฬєя \: » ]]}}$

The required two digit number is 95

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$\sf \red{Given:}$

$\sf In \: a \: two \:digit \:number, \:the \: sum \: of \: two \: digits$ $\sf of \:which \:is \:14 \:and \: if \:29 \:is \:substracted$ $\sf \:from \: the \:number, \:the \: two \:digits \: will \: be \: equal.$

$\sf\red{To \:find:}$

$\sf the \: two \:digit \: number$

$\huge{\underline{\mathtt{\red{S}\pink{O}\green{L}\blue{U}\purple{T}\orange{I}\red{O}{N}}}}$

$\sf Let \:the \:digit \: at \: 10s \: place \: in \:the \: two \: digits \: number = X$

$\sf The \: place \:value \:of \:X = 10 \:× \:X = 10X$

$\sf Let \:the \:digit \:at \:ones \: place \: in \: the \: two \: digits \: number = Y$

$\sf The \:place \: value \:of Y = Y×1 = Y$

$\sf Then , \: The \: two \:digits \: number = 10X+Y$

$\sf blue{Given \:that:}$

$\sf Case -1:$

$\sf The \:sum \:of \: two \: digits = 14$

$\sf X+Y = 14 ------------(1)$

$\sf Case -2:-$

$\sf If \:29 \:is \: subtracted \:from \:the \:number \: then \: the \: two \:digits \:will \:be \: equal$

$\sf ⟹ (10X+Y)-29 =10D+D (D \:is \: some \: digit)$

$\sf ⟹ 10X+Y-29 = 11D$

$\sf ⟹ 10X +Y = 11D+29--------(2)$

$\sf By \:Subtracting \: (1) \: from \:(2) \:we \: get$

$\sf 10X +Y = 11D +29$

$\sf X+Y = 14$

(-)

_______________

$\sf 9X +0 = 11D +29-14$

________________

$\sf ⟹ 9X = 11D+29-14$

$\sf ⟹ 9X = 11D +15$

⟹ $\ X = \dfrac{11D+15}{9}$

If D = 1 then $\ X= {\dfrac{11+15}{9} = \dfrac{26}{9}}$

$\sf The \:digit \: can \:not \:be \: a \: fraction$

If D = 2 then $\ X= {\dfrac{22+15}{9} = \dfrac{37}{9}}$

$\sf If \: we \: continue \: like \: this ...$

If D = 6 then $\ X= {\dfrac{66+15}{9} = \dfrac{81}{9}}= 9$

$\sf So \: we \:get \: a \: natural \: number$

$\sf Therefore, \: X = 9$

$\sf putting \: the \:value \: of \: X \: in \: (1) ,we \: get$

$\sf ⟹ 9+Y = 14$

$\sf ⟹ Y = 14-9$

$\sf ⟹Y = 5$

$\sf X = 9 \:and Y = 5$

$\sf The \: required \:two \:digit \:number \:is \:95$