Question

In a two digit number, digits in the units place is twice the digit in tens place. if 27 is added to it, the digits are reversed. Find the number
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Answer 1

Required solution -

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ There is a two digit number.

★ In a two digit number, digits in the units place is twice the digit in tens place.

★ 27 is added to it, the digits are reversed.

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ The original number.

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The original number = 36

${\large{\bold{\rm{\underline{Assumptions}}}}}$

★ Ten's digit = a

★ Unit's digit = 2a

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ As it's already given that in a two digit number, digits in the units place is twice the digit in tens place. If 27 is added to it, the digits are reverse. Henceforth,

Ten's place -

↝ Required number = 10a + 2a

↝ Required number = 12a

On Interchanging -

↝ Required number = 10(2a)+a

↝ Required number = 20a + a

↝ Required number = 21a

According to the question -

↝ 12a + 27 = 21a

↝ 27 = 21a - 12a

↝ 27 = 9a

↝ 27/9 = a

↝ 3 = a

↝ a = 3

Henceforth, required answer -

↝ 12 × 3

↝ 36

Answer 2

Step-by-step explanation:

$\sf\color{red}Given\:that$

★ There is a two digit number.

★ In a two digit number, digits in the units place is twice the digit in tens place.

★ 27 is added to it, the digits are reversed.

★ The original number.

★ The original number = 36

★ Ten's digit = a

★ Unit's digit = 2a

~ As it's already given that in a two digit number, digits in the units place is twice the digit in tens place. If 27 is added to it, the digits are reverse. Henceforth

$\sf\color{red}Ten's\: place$

↝ Required number = 10a + 2a

↝ Required number = 12a

$\sf\color{red}On\: Interchanging -</p><p>$

↝ Required number = 10(2a)+a

↝ Required number = 20a + a

↝ Required number = 21a

$\sf\color{red}According\: to\: the\: question -$

↝ 12a + 27 = 21a

↝ 27 = 21a - 12a

↝ 27 = 9a

↝ 27/9 = a

↝ 3 = a

↝ a = 3

$\sf\color{red}Henceforth,\: required\: answer -</p><p>$

↝ 12 × 3

↝ 36