Question

The units place digit of a two digit number is four times the digits in the tens place . if the digits are reversed and the original number is subtracted from the new number , the difference is 54 . find the original number​

Answer 1

Answer:

Let the tens place digit be a, so the unit place digit should be 4a. And number should be a 4a, or, a(10) + 4a = 14a.

When digits are reversed, new number is a 4a, or, 10(4a) + a = 41a

According to question, if the digits are reversed and the original number is subtracted from the new number, the difference is 54.

= > 41a - 14a = 54

= > 27a = 54

= > a = 2

Hence the desired number is 14a = 14(2) = 28 Required number is 28.

Answer 2

$\huge\star \: {\sf{\underline{\orange{SolUtion:-}}}}$

${\tt{\red{Let \:the \: tens \:digits \: be \: a, \: so \: the \: unit \:place \:digits \: be\: 4a.}}}$

${\tt{\pink{The \: number \: should \: be = 4a}}}$

${\tt{\pink{By, \: reversing \: digits \: we \:get ,}}}$

${\tt{\pink{or, \: 10(4a) + a = 41a}}}$

${\tt{\underline{A.T.Q}}}$

${\tt{\blue{ If \: Reversing \: digits \:are \: subtracted \: from \: the \: new \: number \: the \: difference\: is \: 54,}}}$

${\implies{\tt{\pink{41a - 14a = 54}}}}$

${\implies{\tt{\pink{27 a = 54}}}}$

${\implies{\tt{\pink{a = \cancel\frac{54}{27} = 2}}}}$

$\boxed {\green{\therefore{ a =2}}}$

${\tt{\purple{Hence\:,the \: original \: number \: is \: 14 a }}}$

${\tt{\purple{putting\:,the \: value\: of \: a \: we get, 14a = 14(2) = 28}}}$

$\boxed {\green{ \: The \: original \: number = 28}}$