Question

A two digit number is seven times the sum of it's digits. The number formed by reversing the digits is 18 less than the original number. Find the number.​

Answer 1

Given :

• A two digit number is seven times the sum of it's digits.

• The number formed by reversing the digits is 18 less than the original number.

To find :

• The required number =?

Step-by-step explanation :

Let x be the digit at ten's place and y be the digit at units place.

Then the number is 10x + y.

According to the first condition of the problem,

10x + y = 7 ( x + y)

10x + y = 7x + 7y

3x = 6y

x = 2y ..... (i)

The number formed by reversing the digits is 10 y + x.

According to the second condition of the problem,

10y + x = (10x + y) - 18

10y - y = 10x - x - 18

9y = 9x - 18

y = x - 2

y = 2y - 2 [Using (i)]

y = 2.

From (i), x = 2 × 2 = 4.

Hence, the required number is 42.

Answer 2

⠀⠀ ☛...Given...☚⠀ ⠀

✰✰⠀A two digit number is seven times the sum of its digit...

✰✰ ⠀The number formed by reversing the digit is 18 less than the original number...

⠀ ⠀ ☛...To find...☚⠀ ⠀

✰✰⠀The original number...

⠀⠀⠀☛...SoLution...☚ ⠀⠀

Let the two digit number be 10x + y...

⠀⠀ ⠀---☛⠀In case 1st...

• 10x + y = 7 ( x + y )
• 10x + y = 7x + 7y
• 10x - 7x = y - 7y
• 3x = 6y
• x = 2y

⠀⠀⠀⠀---☛ ⠀In case 2nd...

• 10x + y - 18 = 10y + x
• 10x - x + y - 10y = 18
• 9x - 9y = 18
• 9 ( x - y ) = 18
• x - y = 18 / 9
• x - y = 2 _____ eq 1...

Substituting value of x in the following equation...

• x - y = 2
• 2y - y = 2
• y = 2

Put value of y in the equation 1...to find the value of x...

• x - y = 2
• x - 2 = 2
• x = 2 + 2
• x = 4

Therefore, the two digit number will be 42...

________verification_______

⠀⠀⠀⠀ ⠀ ⠀10x + y = 42

⠀ ⠀⠀⠀⠀⠀10 ( 4 ) + ( 2 ) = 42

⠀⠀⠀⠀ ⠀ ⠀40 + 2 = 42

⠀ ⠀⠀⠀⠀⠀⠀42 = 42

⠀ ⠀ ⠀ ⠀⠀L.H.S. = R.H.S.⠀

_______Hence verified_____