Question

solve this question ​

Answer 1

• The number = 28.

Given :–

• The sum of a number of two digits and of the number formed by reversing the digits = 110.
• The difference of the digits = 6.

To Find :–

• The number.

Solution :–

Let,

The unit's place digit be x.

The ten's place digit be y.

So,

The number = x + 10y

By reversing the digits = 10x + y

First we need to find the value of x.

According to the question,

➥ (x + 10y) + (10x + y) = 110

➥ 11x + 11y = 110

Take 11 as a common,

➥ 11(x + y) = 110

➥ x + y = $\sf \cancel\dfrac{110}{11}$

➥ x + y = 10 –––––(1)

Also given that,

The difference between the digits is 6.

So,

➥ x – y = 6 –––––(2)

Add both the equation (1) and (2),

➥ (x + y) + (x – y) = 10 + 6

➥ x + y + x – y = 16

➥ x + x + y – y = 16

➥ 2x + 0 = 16

➥ 2x = 16

➥ x = $\sf \cancel \dfrac{16}{2}$

➥ x = 8

Now, we need to find the value of y.

So, substitute the value of x in equation (1),

➥ x + y = 10

➥ 8 + y = 10

➥ y = 10 – 8

➥ y = 2

Now, we have to find the number.

So,

The number = x + 10y

Here we have,

• x = 8
• y = 2

➥ 8 + 10 (2)

➥ 8 + 20

➥ 28

Hence,

The number is 28.