Question

the digit in the unit place of a two digit number is equal to the digit in the tens place of one- third of number and the digit in the tens place of the original number is 2 less than the digit in the units place of one- third of the number. if the sum of the digits of the original number is 6 , then what is the number?

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Answer 1

$\bf{\underline{\underline{Answer:}}}$

• The Original number is = 51.

$\bold{\underline {Given:}}$

• The digit in the unit place of a two digit number is equal to the digit in the tens place of one- third of number.

• The digit in the tens place of the original number is 2 less than the digit in the units place of one- third of the number.

• The sum of the digits of the original number is 6

$\bold{\underline {To \:Find:}}$

• The Original number =?

$\bf{\underline{\underline{Step\: by\: step \:explanation:}}}$

Let one digit of two digit number=10x+y

when its divides by answer will be =10y+(x+2)

(as told in the question)

= x+ y =6

So, the numbers are x , 6 - x

According to the question :

$\tt \begin{lgathered} \tt \implies \dfrac{10x +( 6 - x)}{3} = 10(6 - x) + (x + 2) \\ \\\implies \tt 10x + 6 - x = 3 \times(( 60 - 10x) + x + 2) \\ \\ \implies\tt 10x + 6 - x = 180 - 30x + 3x + 6 \\ \\ \implies\tt 10x = 180 - 30x + 3x + 6 - 6 +x \\ \\ \implies \tt 10x = 180 - 30x + 4x \\ \\ \implies \tt 10x = 180 - 26x \\ \\ \implies \tt 10x + 26x = 180 \\ \\ \implies \tt 36x = 180 \\ \\ \implies\tt x = \dfrac{180}{36} \\ \\ \implies\tt x = 5\end{lgathered}$

One number x = 5

Then, Second number 6 - x = 6 - 5=1.

The number is = 10x + (6 - x)

=10 × 5 + ( 6 - 5)

=51

Hence, The original number = 51