Question

A number consists of two digits. The digit at tens place is two times the digit at units place. the number formed by reversing the digits is 27 less than the original number. Find the original nuber

Answer 1

Answer:

The original number = 63          

Step-by-step explanation:

Let one's place be y and ten's place be x.

 Number be 10x+y.

Given the digit at ten's place is twice the digit at one's/unit's place.

                 Let x = 2y

• When digits are reversed then the number is 10y+x.

• When the digits are reversed then the number formed is 27 less than the original number.

                  10y+x = (10x+y) - 27

               substitute x = 2y

                10y+2y = (10(2y)+y)-27

                      12y = 20y+y-27

                       12y = 21y-27

                12y-21y = -27

                       -9y = -27

                          y = -27/-9

                          y = 3

        now substitute y = 3 in x = 2y

                             x = 2(3)

                             x = 6

        substitute x = 6 and y = 3 in 10x+y

      now the number will be 10x+y = 10(6) + (3)

                                                         = 60+3

                                                         = 63         

            Hence, The original number = 63

         

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Answer 2

Answer:

The original number is 63.

Step-by-step explanation:

Let the digit in unit's place be $y$ and the digit in ten's place be $x$.

Then the number can be written as $10x+y$.

Given that the digit at ten's place is two times the digit at unit's place.

Hence $x = 2y$

When the digits are reversed, then the number can be written as $10y+x$.

Given that when the digits are reversed, the number is 27 less than the original number.

This gives us,

$10y+x = (10x+y) - 27$

Using, $x = 2y$

$10y+2y = (10\times 2y+y) - 27$

$\implies 12y = (20y+y) - 27 \implies 12y = 21y - 27$

$\implies 21y- 12y = 27 \implies 9y = 27 \implies \dfrac{ 27 }{9} =3$          

Substituting $y = 3$ in $x = 2y$

gives $x = 2\times 3=6$

Thus, the original number is                

$10x+y=10\times 6+3= 60+3 = 63$    

Therefore, the original number is 63.

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