Question

a number consists of two digits whose sum is 9. if 27 is subtracted from the number its digits are reversed. find the nummber

Answer 1

Answer:

Step-by-step explanation:

Let the number =ab=10a+b

Sum of digits =9

a+b=9

number −27=number with reversrd digits

10a+b−27=10b+a

9(a−b)=27

a−b=3

(a+b)+(a−b)=9+3⇒a=6,b=3

∴  Required number is 63

Answer 2

Answer:

36 or 63 can be the number

Step-by-step explanation:

Assuming

x as tens digit

y as ones digit

Their sum :

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

Number formed :

10x + y

Interchanging the digits :

10y + x

According to the question :

➡ (10x + y) - (10y + x) = 27

➡ 9x - 9y = 27

➡ 9(x - y) = 27

➡ x - y = 27/9

➡ x - y = 3 ..... (ii)

Subtracting both the equation :

$\bf \: x + y = 9 \\ { \underline{ \bf{x - y = 3}}} \\ \implies \bf \: 2x = 6 \\ \implies \bf \: x = 3$

Substituting the value of x in equation (i) :

➡ x + y = 9

➡ 3 + y = 9

➡ y = 6

Hence

The number can be 10x + y

or, 10(3) + 6

or, 36 either 63