Question

sum of the digits of a two number is 12, the given number exceeds the number obtained by interchanging the digits by 36. Find the given number

Answer 1

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Answer 2

A N S W E R :

• Original number is 84.

$\underline{\frak{\qquad Given :\qquad}}$

• Sum of the digits of a two number is 12, the given number exceeds the number obtained by interchanging the digits by 36.

$\underline{\frak{\qquad To \:Find :\qquad}}$

• The original number = ?

$\underline{\frak{\qquad Solution :\qquad}}$

$\large\bigstar\:\underline{\textsf{Original Number :}}$

$:\implies\sf Original \: Number = 10(12 - x) + x$

$:\implies\sf Original \: Number = 120 - 10x + x$

$:\implies\sf Original \: Number = 120 - 9x$

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$\large\bigstar\:\underline{\textsf{Interchanged Number :}}$

$:\implies \sf Interchanged \: Number = 10x + 12 - x$

$:\implies \sf Interchanged \: Number = 9x + 12$

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☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$\dashrightarrow\:\:\sf Original \: Number - 36 = Interchanged \: Number$

$\dashrightarrow\:\:\sf 120 - 9x - 36 = 9x + 12$

$\dashrightarrow\:\:\sf 84- 9x = 9x + 12$

$\dashrightarrow\:\:\sf 84- 12 = 9x + 9x$

$\dashrightarrow\:\:\sf 72 = 18x$

$\dashrightarrow\:\:\sf x = \dfrac{72}{18}$

$\dashrightarrow\:\: \underline{ \boxed{\sf x = 4}}$

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$\large\therefore\: \underline{\textsf{The given original number is :}}$

$\bullet\:\textsf{Original Number = 120 - 9x = 120 - 9(4) = 120 - 36 = \textbf{84}}$

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