Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the numbers
Find the number.
.
digits are reversed. Find the number​

Answer 1

✪ Question ✪

A number consists of two digits whose sum is 9. If 27 is subtracted from the number, the digits are reversed. Find the number.

✪ Given ✪

• The sum of the two digits = 9
• If 27 is subtracted from the numbers, the digits are reversed.

✪ To find ✪

The number.

✪ Solution ✪

Let the ones digit be x.

So, the tens digit = (9-x).

According to condition,

{10(9-x)+x} - {10x+(9-x)} = 27

→ (90-10x+x) - (10x+9-x) = 27

→ (90-9x) - (9x+9) = 27

→ 90-9x-9x-9 = 27

→ -18x+81 = 27

→ -18x = 27-81

→ -18x = -54

→ 18x = 54

→ x = 54/18

→ x = 3

✪ Hence ✪

x = 3

☞ Ones digit = x = 3.

☞ Tens digit = (9-x) = (9-3) = 6

✪ Therefore ✪

The required number is 63.

________________________________

✪ Verification ✪

63-27 = 36

→ 36 = 36

Hence, L.H.S = R.H.S.

Done ࿐

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