Question

18. The sum of a two-digit number and the number obtained by reversing
the order of its digits is 121, and the two digits differ by 3. Find the
number
​

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ number \ is \ 74}$

$\sf\orange{Given:}$

$\sf{\implies{The \ sum \ of \ a \ two \ digit \ number}}$

$\sf{and \ number \ obtained \ by \ reversing \ the}$

$\sf{order \ of \ it's \ digits \ is \ 121.}$

$\sf{\implies{The \ two \ digit \ differ \ by \ 3}}$

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

$\sf{The \ two \ digit \ number.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ the \ digit \ in \ the \ ten's \ place \ be \ x}$

$\sf{and \ the \ digit \ in \ the \ unit's \ place \ be \ y.}$

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

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

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

$\sf{(10x+y)+(10y+x)=121}$

$\sf{11x+11y=121}$

$\sf{11(x+y)=121}$

$\sf{x+y=\frac{121}{11}}$

$\sf{\therefore{x+y=11...(1)}}$

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

$\sf{x-y=3...(2)}$

$\sf{Add \ equations \ (1) \ and \ (2)}$

$\sf{x+y=11}$

$\sf{+}$

$\sf{x-y=3}$

______________

$\sf{2x=14}$

$\sf{\therefore{x=\frac{14}{2}}}$

$\boxed{\sf{\therefore{x=7}}}$

$\sf{Substitute \ x=7 \ in \ equation (1)}$

$\sf{7+y=11}$

$\sf{y=11-7}$

$\boxed{\sf{\therefore{y=4}}}$

$\sf{Original \ number=10(7)+4=74}$

$\sf\purple{\tt{\therefore{The \ number \ is \ 74}}}$