Question

Sum of two digit of a number is 11.If the digits are interchanged the number so got is 27 more than it.Find the numbers?​

Answer 1

Answer:

The original number is 47.

Step-by-step explanation:

Given that:

Sum of two digit of a number is 11.

The digits are interchanged the number so got is 27 more than it.

To Find:

The original number.

Let us assume:

Tens digit be x.

Ones digit be y.

Original number = 10x + y

When digits are interchanged:

New number = 10y + x

Finding the value of x and y:

Sum of two digit.

⟶ x + y = 11

⟶ x = 11 - y ════(i)

When the digits are interchanged.

⟶ 10x + y + 27 = 10y + x

Substituting the value of x from eqⁿ (i).

⟶ 10(11 - y) + y + 27 = 10y + 11 - y

⟶ 110 - 10y + y + 27 = 9y + 11

⟶ 137 - 9y = 9y + 11

⟶ 9y + 9y = 137 - 11

⟶ 18y = 126

⟶ y = 126/18

⟶ y = 7

In equation (i).

⟶ x = 11 - y

Substituting the value of y.

⟶ x = 11 - 7

⟶ x = 4

Finding the original number:

→ Original number = 10x + y

→ Original number = 10(4) + 7

→ Original number = 40 + 7

→ Original number = 47

Answer 2

$\huge {\underline { \red}\bold \color{cyan}{AnSwEr ♡}}$

Given:-

• Sum of two digit of a number = 11
• The digits are interchanged and the number so got is 27 more than it.

To Find:-

• The Numbers

Solution:-

Let’s represent the tens digit with a and the ones digit with b.

As given,

$⟹\:a + b = 11⟹a+b=11$

$⟹\:b = 11-a⟹b=11−a \: \: \: (1)$

The number will be "10a + b".

As given in the question the digits are interchanged. So, According to question

$⟹\:10a + b = 10b + a + 27⟹10a+b=10b+a+27$

$⟹\:10a + (11 - a) = 10(11 - a) + a + 27⟹10a+(11−a)=10(11−a)+a+27 {from 1}$

$⟹\:10a + 11 - a = 110 - 10a + a + 27⟹10a+11−a=110−10a+a+27</p><p>⟹\:9a + 11 = 110 - 9a + 27⟹9a+11=110−9a+27</p><p>⟹\:9a + 11 = 137 - 9a⟹9a+11=137−9a</p><p>⟹\:18a + 11 = 137⟹18a+11=137</p><p>⟹\:18a = 126⟹18a=126</p><p>⟹\:a = 126/18⟹a=126/18$

${\boxed{\blue{⟹\:a = 7}}}$

Putting the value of a in {1},

$⟹\:b = 11-a⟹b=11−a$

$⟹\:b = 11-7⟹b=11−7$

${\boxed{\orange{⟹\:b = 4}}}$

So, the interchanged number is 10a + b = 74.

On interchanging it we get the original number which is 47.

• Hence, The original number is 47.