One of the two digits of a two-digit number is three times the other digit If you interchange the digits of this two-digit number and add the resulting number to the original number, you get $88$. What is the original number?

Given: One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88.

To do: To find the Number

Solution:

Let the digits at tens place be $x$.

And ones place be $3x$.

Original Number $=10x+3x=13x$

Number after interchanging $=10\times3x+x=30x+x=31x$

According to the Question,

$\Rightarrow $ Original number $+$ New number $=88$

$\Rightarrow  13x+31x=88$

$\Rightarrow  44x=88$

$\Rightarrow  x=\frac{88}{44}$

$\Rightarrow  x=2$

Original Number $=13x=13\times2=26$

Therefore, by considering the tens place and ones place as $3x$ and $x$.

The two digit number obtained is $62$.

Hence, the two-digit number may be $26$ or $62$.
 

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Updated on: 10-Oct-2022

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