Question

The sum of digits of a two digit number is 12. If the number is increased by 18, its digit gets reversed. The number is

Answer 1

EXPLANATION.

Let the digit at tens place be = x

Let the digit at unit place be = y

Original number = 10x + y

reversing number = 10y + x

The sum of digit of a two digit number = 12.

=> x + y = 12 .......(1)

If the number is increased by 18 it's digit reversed.

=> 10y + x = 10x + y + 18

=> 9y - 9x = 18

=> y - x = 2 .......(2)

From equation (1) and (2) we get,

=> 2y = 14

=> y = 7

Put the value of y = 7 in equation (1) we get,

=> x + 7 = 12

=> x = 5

Therefore,

original number = 10x + y = 10(5) + 7 = 57.

Answer 2

Let

• The number be 10x+y

━━━━━━━━━━━━━━━━━

Given:

• Sum of digits of two digits of the number =12
• If number is increase by 18 the digits get reversed.

━━━━━━━━━━━━━━━━━

Need to find :

• The number =?

━━━━━━━━━━━━━━━━━━

SOLUTION:

As per the given information,

$\purple{\boxed{x+y= 12----i}}$

And if number is increase by 18 the digits get reversed. Thus:

10x+y +18 = 10y+ x

⟹ 10x -x + 18 = 10y -y

⟹ 9x + 18= 9y

⟹ 9y - 9x = 18

⟹ y- x = 18/ 9

$\purple{\boxed{\implies y-x=2----ii}}$

━━━━━━━━━━━━━━━━━

Now by adding i and ii we get

(x+y)+(y-x)=12+2

⟹x+ y + y-x = 14

⟹ 2y= 14

⟹$\bold{\purple{y= 7}}$

Now by putting y= 7 in eq ii we get,

7-x=2

⟹ x =7-2

⟹$\bold{\purple{x= 5}}$

The number is:

10x+y

= 10×5 + 7

=57

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Thus the number is $\huge{\red{\bold{\boxed{57}}}}$