Question

The sum of digits of a two digit number is 15.If the number formed by reversing the digits is less than the original number by 27,find the original number​

Answer 1

Answer:

This is the answer of this question.

Answer 2

Given :–

• The sum of digits of a two digit number = 15.
• Number formed by reversing the digits is less than the original number by 27.

To Find :–

• The original number.

Solution :–

Let,

The unit's place be x.

Then the ten's place be 15 – x.

Original number = 10 × (15 – x) + 1 × x

⟹ 150 – 10x + x

• 150 – 9x

By reversing this digits, we get

New number = 10 × x + 1 × (15 – x)

⟹ 10x + 15 – x

⟹ 10x – x + 15

• 9x + 15

According to the question,

Original number – New number = 27

• Original number = 150 – 9x.
• New number = 9x + 15.

Now, put both the values, we get

⟹ [150 – 9x] – [9x + 15] = 27

Open both the brackets.

⟹ 150 – 9x – 9x – 15 = 27

⟹ 135 – 18x = 27

⟹ –18x = 27 – 135

⟹ –18x = –108

⟹ x = $\dfrac{\cancel- \cancel{108}}{\cancel- \cancel{18}}$

Cut the denominator and the numerator by 2, we obtain

⟹ x = $\dfrac{\cancel{54}}{\cancel{9}}$

Cut the denominator and the numerator by 3, we obtain

⟹ x = $\dfrac{\cancel{18}}{\cancel{3}}$

Again, cut the denominator and the numerator by 3, we obtain

⟹ x = 6

Now, we have to find the original number.

Original number = 150 – 9x

⟹ 150 – 9(6)

Now, open the bracket.

⟹ 150 – 54

⟹ 96

Hence,

The original number is 96.