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.
(in one variable)​

Answer 1

Answer:

The required number is 63.

Step-by-step explanation:

Let the ten's digit be y and the unit's digit be x.

Solution:-

Given that,

x + y = 9 .... equation 1

So, the number is 10x + y.

Given, If 27 is substracted from the number, it's digit gets reversed.

Now,

10x + y - 27 = 10x + x

$\implies$ 9x - 9y = 27

$\implies$ x - y = 3 .... equation 2

Now, by adding equation 1 and equation 2 we got,

$\implies$ 2x = 12

$\implies$ x = 12/6

$\implies$ x = 2

Now, by substituting x = 6 in unit's place and we also got y = 3 of ten's digit place.

Required Answer:-

Therefore, the required number is 63.

Answer 2

Answer:

Given :-

• A number consists of two digits whose sum is 9 and 27 is substracted from the number and the digits are reserved.

To Find :-

• What is the number.

Solution :-

Let, the other number is 9 - x

So, the two number is 10(9 - x) + x

And, the number obtained after reversing the digits is 10x + (9 - x)

According to the question,

⇒ 10(9 - x) + x - 27 = 10x + (9 - x)

⇒ 90 - 10x + x - 27 = 10x + 9 - x

⇒ - 10x + x - 10x + x = 9 - 90 + 27

⇒ - 18x = - 54

⇒ x = $\sf\dfrac{\cancel{- 54}}{\cancel{- 18}}$

➾ x = 3

Hence, the required number is,

⇒ 10(9 - x) + x

⇒ 10(9 - 3) + 3

⇒ 10(6) + 3

⇒ 60 + 3

➠ 63

$\therefore$ The required number is 63 .