Question

sum of the digits of a two digit number is 6,When we interchange the digits,it is found that the resulting new number is greater than the original number by 18, what is the two digit number?​

Answer 1

Answer:

Given :-

• Sum of the digits of a two digit number is 6.
• When we interchange the digits, it is found that the resulting new number is greater than the original number by 18.

To Find :-

• What is the two digit number.

Solution :-

Let,

$\mapsto$ Digits at unit's place be x

$\mapsto$ Digits at ten's place will be y

Then, the original number is :

$\leadsto \sf\bold{Original\: number =\: 10x + y}$

According to the question,

$\hookrightarrow$ Sum of the digits of a two digit number is 6.

$\implies \sf x + y =\: 6$

$\implies \sf\bold{\purple{x + y =\: 6\: ------\: (Equation\: No\: 1)}}$

$\hookrightarrow$ When we interchange the digits, it is found that the resulting new number is greater than the original number by 18.

$\implies \sf 10x + y + 18 =\: 10y + x$

$\implies \sf 10x - x + y - 10y =\: - 18$

$\implies \sf 9x - 9y =\: - 18$

$\implies \sf 9(x - y) =\: - 18$

$\implies \sf (x - y) =\: \dfrac{- \cancel{18}}{\cancel{9}}$

$\implies \sf\bold{\purple{x - y =\: - 2\: ------\: (Equation\: No\: 2)}}$

Now, by adding the equation no 1 and 2 we get,

$\implies \sf x + y + x - y =\: 6 + (- 2)$

$\implies \sf x + x {\cancel{+ y}} {\cancel{- y}} =\: 6 - 2$

$\implies \sf 2x =\: 4$

$\implies \sf x =\: \dfrac{\cancel{4}}{\cancel{2}}$

$\implies \sf\bold{\green{x =\: 2}}$

Again, by putting x = 2, in the equation no 1 we get,

$\implies \sf x + y =\: 6$

$\implies \sf 2 + y =\: 6$

$\implies \sf y =\: 6 - 2$

$\implies \sf\bold{\green{y =\: 4}}$

Hence, the required original number is :

$\longrightarrow \sf Original\: Number =\: 10x + y$

$\longrightarrow \sf Original\: Number =\: 10(2) + 4$

$\longrightarrow \sf Original\: Number =\: 20 + 4$

$\longrightarrow \sf\bold{\red{Original\: Number =\: 24}}$

$\therefore$ The original number is 24.

Answer 2

ANSWER:-

THE NUMBER IS 24

QUESTION:-

sum of the digits of a two digit number is 6,When we interchange the digits,it is found that the resulting new number is greater than the original number by 18, what is the two digit number?​

GIVEN:-

1)Sum of the digits of a two digit number is 6.

2)When we interchange the digits, it is found that the resulting new number is greater than the original number by 18

TO FIND:-

THE NUMBER

EXPLANATION:-

LET THE DIGIT AT TENS PLACE =X

AND AT ONES =6-X

==>10x+6-x

==>9x+6(original number)

on interchanging the digit :

tens place =6-x

ones place=x

number =10(6-x)+x

===>60-10x+x

===>60-9x(new number )

so to make the equation equal we will add 18 to original number:-

ATQ,

9x+6+18=60-9x

9x+24=60-9x

9x+9x=60-24

18x=36

x=2

so tens digit of number is x=2

and ones digit if 6-x==>6-2==>4

and the number if 24