Question

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

Answer 1

Answer:

The original number = 63

The reversed number = 36

Step-by-step explanation:

The more easiest and less time-consuming method to solve this question is by guessing the numbers.

If you guess which double-digit numbers whose digits add up to 9, you'll see that there are only 10 numbers that satisfy the condition. Those numbers are 09, 18, 27, 36, 45, 54, 63, 72, 81, 90.

Now all you have to do is subtract 27 from either 54, 63, 72, 81, 90.

(You can't choose the other numbers because then the condition is saying that it shouldn't be greater than the original number.)

When you subtract 27 from 63, you get 36, which is nothing but the reversed digits of the original number.

And voila! you got the answer in a faster method!

Hope this answer helped you!

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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