Question

Points 50


sum of the digit of a two digit number is 12. New number formed by reversing the digit is greater than the original by 54. Find the original number.

Solve by both one and two variable.

and plz explain every point of your solution

Answer 1

Answer:

Let the digits be = x and y

x + y = 12 ...(2)

Second equation :-

10y + x = 10x + y + 54

=> 9y - 9x = 54

=> y - x = 6

=> y = 6 + x ... (1)

(1) in (2)

=> x + 6 + x = 12

=> 2x = 6

=> x = 3

y = x + 6 = 9

Number = 39

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Alternate method :-

Let the digits be = y, 12 - y ( y = unit digit)

=> According to question :

10y + (12 - y) = 10 (12 - y) + y + 54

=> 10y + 12 - y = 120 - 10y + y + 54

=> 9y + 9y = 54 - 12 + 120

=> 18y = 162

=> y = 9

12 - y = 3

Number = 39

Answer 2

Step-by-step explanation:

Let the no. of the 2 digits be 10x+y

sum of the digits is 15

therefore,

x+y=15-----》1

no formed by reversing the digit =(10y+x)

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

9x - 9y = 27------》2

equation 2 dividing by 3

3x-3y=9------》3

again dividing it by 3

x-y=3------》4

solving by 1 and 4

x=9

y=6

the original no is 10x+y

=》10(9)+6

=》90+6

=》96

Hope it helps ❤