Question

the sum of the digits of a two-digit number is 17 the new number formed by receiving the digital is greater than the original number by 9 find the original number​

Answer 1

CORRECT QUESTION:

Q: The sum of the digits of a two-digit number is 17. The new number formed by reversing the digits is greater than the original number by 9. Find the original number.

Answer:

• The original number = 89

Step-by-step explanation:

Let us assume:

• Tens digit of a number be A.
• Ones digit of a number be B.

Number formed:

• Original number = 10A + B
• Reversed number = 10B + A

Given that:

• The sum of the digits of a two-digit number is 17.

⇒ A + B = 17

⇒ A = 17 - B _____(i)

• The new number formed by reversing the digits is greater than the original number by 9.

⇒ 10A + B + 9 = 10B + A _____(ii)

To Find:

• The original number.

Finding the values of A and B:

• In equation (ii).

⇒ 10A + B + 9 = 10B + A

• Substituting the value of A from eqⁿ (i).

⇒ 10(17 - B) + B + 9 = 10B + (17 - B)

⇒ 170 - 10B + B + 9 = 10B + 17 - B

⇒ - 10B + B - 10B + B = 17 - 170 - 9

⇒ - 18B = - 162

• Minus sign cancelled both sides.

⇒ 18B = 162

⇒ B = 162/18

⇒ B = 9

• Now, In equation (i).

⇒ A = 17 - B

• Substituting the value of B.

⇒ A = 17 - 9

⇒ A = 8

Finding the original number:

⇒ Original number = 10A + B

• Substituting the values of A and B.

⇒ Original number = 10(8) + 9

⇒ Original number = 80 + 9

⇒ Original number = 89

Answer 2

Answer:

Given :-

• The sum of the digits of a two digit number is 17. The new number formed by reversing the digits Is greater than the original number by 9.

To Find :-

• What is the original number.

Solution :-

Let, the digits at ten place be x

And, the digits at unit place will be y

Then, the original number is 10x + y

And, the reversed number is 10y + x

➦ x + y = 17 -------- (Equation no 1)

Again,

⇒ 10x + y + 9 = 10y + x

⇒ 10x - x - 10y + y = - 9

⇒ 9x - 9y = - 9

➦ x - y = - 1 --------- (Equation no 2)

Now, by adding the equation no (1) and (2) we get,

⇒ x + y + x - y = 17 + (- 1)

⇒ x + x + y - y = 17 - 1

⇒ 2x = 17 - 1

⇒ 2x = 16

⇒ x = 16/2

➠ x = 8

Again, by putting x = 8 in the equation no (1) we get,

↦ x + y = 17

↦ 8 + y = 17

↦ y = 17 - 8

➠ y = 9

∴ The original number is 89 .