Question

sum of digital of a two digit number is 11. If the digitals are interchange the number so got is 27 more than it. Find the numbers?
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Answer 1

Answer:

The number is 47

Step-by-step explanation:

Let,

Units digit = x

Tens digit = 11 - x

Original number :

⇒ 10 (11 - x) + x

⇒ 110 - 10x + x

⇒ 110 - 9x

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

⇒ 10x + 11 - x

⇒ 10x - x + 11

⇒ 9x + 11

★ According to the Question :

⇒ (110 - 9x) + 27 = 9x + 11

⇒ 110 - 9x + 27 = 9x + 11

⇒ 110 + 27 - 9x = 9x + 11

⇒ 137 - 9x = 9x + 11

⇒ 137 - 11 = 9x + 9x

⇒ 126 = 18x

⇒ x = 126 / 18

⇒ x = 7

Units digit = 7

Tens digit = 11 - x

⇒ 11 - 7 = 4

Tens digit = 4

Therefore, the number is 47

Answer 2

Answer:

Question :-

• Sum of digital of a two digit number is 11. If the digitals are interchange the number so got is 27 more than it. Find the numbers?

Given :-

• Sum of digital of a two digit number is 11. If the digitals are interchange the number so got is 27 more than it.

Find Out :-

• Find the numbers?

Solution :-

Let :

• Tens digit be x.
• Ones digit be y.
• Original number = 10x + y

When digits are interchanged:

$\curlyeqsucc$ New number = 10y + x

Sum of two digit :

$\leadsto$ x + y = 11

$\leadsto$ x = 11 - y ---------(Eqn no 1)

When the digits are interchanged :

$\leadsto$ 10x + y + 27 = 10y + x

Substituting the value of x from eqn (i) we get that ,

$\leadsto$ 10(11 - y) + y + 27 = 10y + 11 - y

$\leadsto$ 110 - 10y + y + 27 = 9y + 11

$\leadsto$ 137 - 9y = 9y + 11

$\leadsto$ 9y + 9y = 137 - 11

$\leadsto$ 18y = 126

$\leadsto$ y = 126/18

$\leadsto$ y = 7

From the equation 1 we get,

$\leadsto$ x = 11 - y

Substituting the value of y = 7 in the equation no 1 we get,

$\leadsto$ x = 11 - 7

$\leadsto$ x = 4

Let's finding the original number:

$\implies$ Original number = 10x + y

$\implies$ Original number = 10(4) + 7

$\implies$ Original number = 40 + 7

$\implies$ Original number = 47

Therefore, the numbers is 47.