Question

Sum of the digits of a two digit number is 9.when we interchange the digits, it is found that the resulting new number is greater than the original number by 27.what is the two digit number?

Answer 1

Heya

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Let the two digit number be xy

ACCORDING TO THE QUESTION

x + y = 9 .... Equation ( i )

10y + x = 27 + 10x + y

=>

9y - 9x = 27

=>

y - x = 3 .... Equation ( ii )

ADD EQUATION i and ii

2y = 12

=>

y = 6 And x = 3

So, the two digit number is 36

Answer 2

Given,

• Sum of the two digits of a two digit number is 9.
• When we interchange the digits then the resulting number is greater then the original number by 27.

To Find,

• The two digit number

Solution,

⇒Suppose the ten's digit be a

And , Suppose the one's digit be b

Therefore ,

Two digit number = (10a +b)

Interchanging Number = (10b + a)

According to the First Condition :-

• Sum of the two digits of a two digit number is 9

$\implies \sf{a + b = 9}$

$\implies \boxed{\sf{a = 9 - b}}$

According to the Second Condition :-

• When we interchange the digits then the resulting number is greater then the original number by 27.

$\implies \sf{10b + a = 10a + b +27}$

$\implies \sf{10b - b = 10a - a + 27}$

$\implies \sf{9b = 9a + 27}$

$\implies \sf{9b = 9(9 - b) + 27}$

(Put the value of a From First Condition)

$\implies \sf{9b = 81 - 9b + 27}$

$\implies \sf{ 9b + 9b = 81 + 27}$

$\implies \sf{ 18b = 108}$

$\implies \sf{ b = \dfrac{108}{18}$

$\implies \boxed{\sf{b = 6}}$

Now Put value of b in First Condition :-

$\implies \sf{a = 9 - b}$

$\implies \sf{a = 9 - 6}$

$\implies \boxed{\sf{ a = 3}}$

Therefore ,

$\star{\boxed{\sf{\purple{Two \ Digit \ Number = 10a + b = 10(3) + 6 = 36}}}}$

$\rule{200}2$