Question

the onse digit ofa 2 digit number is twice the tens digit. when the number formed by reversing the digits is added to the orignal number the sum is 99. find the original number​

Answer 1

Given Question :-

• The ones digit of a 2 digit number is twice the tens digit. When the number formed by reversing the digits is added to the orignal number the sum is 99. Find the original number.

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Solution :-

$\tt \:  Lets \: tens \: digit \: of \: two \: digit \: number \: be \: x$

$\tt \:  So, \: ones \: digit \: of \: two \: digit \: number \: be \: 2x.$

$\tt \:  ⟼Number \: formed = 10 \times x + 2x \times 1 = 12x$

$\tt \:  ⟼Reverse \: number = 10 \times 2x + x \times 1 = 21x$

☆ Now, According to statement, the number formed by reversing the digits is added to the orignal number, we get sum as 99.

$\tt\implies \:21x + 12x = 99$

$\tt \:  ⟼ \: 33x = 99$

$\tt \:  ⟼ \: x \: = \dfrac{ \cancel{99} \: \: \: \: \: ^ 3}{ \cancel{33} \: \: \: \: \: \: \: }$

$\tt\implies \: \: x \: = \: 3$

$\begin{gathered}\begin{gathered}\tt Hence, \: Number \: formed = \begin{cases} &\sf{12x = 12 \times 3 = 36} \end{cases}\end{gathered}\end{gathered}$