Question

The digit in the units place of a 2 digit no. is 4 times the digit in the tens place, the no. obtained by reversing the digits, exeeds the given no. by 54. Find the given no.



PLEASE ANSWER​

Answer 1

Answer:

$\sf{The \ given \ number \ is \ 28.}$

Given:

• The digit in the unit's place of a two digit number is four times the digit in the ten's place.

• The number obtained by the reversing the digits, exceeds the given number by 54.

To find:

• The given number.

Solution:

$\sf{Let \ the \ ten's \ place \ of \ the two \ digit}$

$\sf{number \ be \ x \ and \ unit's \ place \ be \ y.}$

$\sf{According \ to \ the \ first \ condition}$

$\sf{y=4x}$

$\sf{\therefore{4x-y=0...(1)}}$

$\sf{According \ to \ the \ second \ condition}$

$\sf{Original \ number=10x+y}$

$\sf{Number \ with \ reversed \ digits=10y+x}$

$\sf{(10x+y)+54=(10y+x)}$

$\sf{\therefore{9x-9y=-54}}$

$\sf{\therefore{x-y=6...(2)}}$

$\sf{Subtract \ equation (2) \ from \ equation (1)}$

$\sf{4x-y=0}$

$\sf{-}$

$\sf{x-y=-6}$

______________

$\sf{3x=6}$

$\sf{\therefore{x=2}}$

$\sf{Substitute \ x=2 \ in \ equation \ (1)}$

$\sf{4(2)-y=0}$

$\sf{\therefore{y=8}}$

$\sf{The \ original \ number=20+8=28}$

$\sf\purple{\tt{\therefore{The \ given \ number \ is \ 28.}}}$