Question

The sum of the digits of a two-digit number is 10. If 18 is subtracted from it, will the digits in the resulting number be equal?​

Answer 1

Answer:

The number is 73.

Explanation :

Given :

The sum of the digits of a two-digit number is 10.

To Find :

The number.

Solution :

★ Consider the -

Unit number as - y

Number at ten's place as - x

The resulting equal digits as - z

It implies that :

⇒ x + y=10

⇒ y = 10 - x

If 18 be subtracted from it, It will be,

⇒ 10x + y - 18 = 10z + z  

⇒ 10x + y = 11z + 18

Substitute the value of  (10-x) for y,

⇒ 10x + (10-x) = 11z + 18

⇒ 10x - x = 11z + 18 - 10

⇒ 9x = 11z + 8

The values of :

• x = 7
• y = 3
• z = 5.

These values form the number - 73  

$\rule{300}{1.5}$

★ Verification :

Given in Question:

If 18 be subtracted from it, the digits in the resulting number will be equal.

⇒ 73 - 18 = 55

Answer 2

$\large{\mathfrak{\underline{\underline{Answer :-}}}}$

Let the once's place be a .

Let the ten's place be b .

Let the resulting digit be c .

_______________________

A. T. Q ,

⇒ a + b = 10.......(1)

From equation 1

⟹ a = 10 - b .......(2)

__________________________

\ We need to subtract 18 \

–––––––––––––––––––

⟹ 10b + a = 10c + c

⟹ 10b + a = 11c + 18

[Substitute value of a]

⟹ 10b + (10-b) = 11c + 18

⟹ 10b - b = 11c + 18 -10

⟹ 9b = 11c + 8

___________________________

So, values are :-

✯a = 7

✯b = 3

✯y = 5