Question

The sum of a two dight number and the numeber obtained by reversing the dight is 66 if the dight of the numeber differ find the numeber how many such number are tere

Answer 1

QUESTION

The sum of a two digit number and the number obtained by reversing the digit is 66. If the digits of the number differ by 2, find the number how many such numbers are there.

SOLUTION

Given

The sum of a two digit number and the number obtained by reversing the digit is 66.

$\implies 10x+y+10y+x=66$

$\implies 11x+11y=66$

$\implies x + y = 6 --(1)$

The digits of the number differ by 2.

$\implies x-y = 2 , x>y$

Solving, the 2 equations we get,

$x+y=6\\\underline{x-y=2}\\\underline{\underline{2x=8}}\\\implies x = 4$

From equation (1), we get,

$\implies 4+y=6\\\implies y = 2$          

If x < y, then

x = 2, y = 4

$\boxed{\boxed{\bold{Therefore, \ there \ are \ 2 \ numbers \ possible \ : \ 42 \ and \ 24}}}}}$

                                                         

Answer 2

Correct Question:

The sum of a two dight number and the number obtained by reversing the digit is 66. If the dight of the numeber differ by 2. Findhow many numbers are formed?

Answer:

Let ten’s and the unit’s digits be x and y.

⋆ Original Number = 10x + y

But when the digits are reversed, x becomes the unit’s digit and y becomes the ten’s digit.

⋆ Reverse Number = 10y + x

☯ According to the Question :

⇢ (10x + y) + (10y + x) = 66

⇢ 11(x + y) = 66

⇢ x + y = 6 — eq. ( I )

Given that the digits differ by 2, Therefore ;

Either : x – y = 2 — eq. ( II )

Or : y – x = 2 — eq. ( III )

______________________

☢ Adding eq. ( I ) & eq. ( II ) :

⇾ x + y = 6

⇾ x – y = 2

─────────

⇾ 2x = 8

• Dividing both term by 2

⇾ x = 4

⋆ Using value of x in eq. ( I ) :

⇴ x + y = 6

⇴ 4 + y = 6

⇴ y = 6 – 4

⇴ y = 2

∴ In this case, the number will be 42.

━━━━━━━━━━━━━━━━━━━━

☢ Adding eq. ( I ) & eq. ( III ) :

⇾ x + y = 6

⇾ y – x = 2

─────────

⇾ 2y = 8

Dividing both term by 2

⇾ y = 4

⋆ Using value of x in eq. ( I ) :

⇴ x + y = 6

⇴ x + 4 = 6

⇴ x = 6 – 4

⇴ x = 2

∴ In this case, the number will be 24.