Question

the sum of a two digit number and the number obtained by reversing the order of digits is 132. if 12 is added to the number ,new number becomes 5 times the sum of the digits of the original number.find the number.

Answer 1

Dear student
$$\begin{gathered} ThereisamistakeinyourquestionIf12beaddedshouldbethere. \\ Letthedigitsinthenumberbexandy. \\ sothenumberis10x+y. \\ Oninterchangingthenumberbecomes10y+x \\ Itisgiventhatthesumofthesetwonumbersis132. \\ or10x+y+10y+x=132 \\ \Rightarrow 11x+11y=132 \\ \Rightarrow x+y=12...\left(1\right) \\ Now,itisgiventhat \\ 10x+y+12=5\left(x+y\right) \\ \Rightarrow 10x+y+12=5\left(12\right) \\ \Rightarrow 10x+y+12=60 \\ \Rightarrow 10x+y=48 \\ \Rightarrow 10x+12-x=48\left[u\sin g1\right] \\ \Rightarrow 9x=36 \\ \Rightarrow x=4 \\ anndy=8 \\ So,thenumberis10\left(4\right)+8=48 \end{gathered}$$
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