Question

The sum of the digits of a two digit
number is 3. If we subtract 9 from the
number, the digits are inter changed
Find the orignal no.​

Answer 1

Given :

• The sum of the digits of a two digit
• number is 3.
• If we subtract 9 from the number, the digits are inter changed.

To Find :

• The orignal number = ?

Solution :

Let ten's digit of two digit number be x and one's digit be y.

It is given that,the sum of the digits of a two digit number is 3. Mathematically it can be expressed as :

• x + y = 3 ....[Equation (I)]

★ Original Number = 10x + y

★ Interchanged Number = 10y + x

★ According to Question now :

→ 10x + y - 9 = 10y + x

→ 10x - x + y - 10y = 9

→ 9x - 9y = 9

→ 9(x - y) = 9

→ x - y = 9 ÷ 9

→ x - y = 1 ......[Equation (II)]

From equation (i) and equation (ii) we get :

→ x + y - x + y = 3 - 1

→ 2y = 2

→ y = 2 ÷ 2

→ y = 1

Now,subsitute the value of y = 1 in equation (i) we get :

→ x + y = 3

→ x + 1 = 3

→ x = 3 - 1

→ x = 2

★ Finding the original number :

→ Original Number = 10x + y

→ Original Number = 10(2) + 1

→ Original Number = 20 + 1

→ Original Number = 21

• Hence,the original number is 21.

Answer 2

$\huge{\boxed{\rm{Question}}}$

The sum of the digits of a two digit number is 3. If we subtract 9 from the number, the digits are inter changed. Find the orignal number.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• The sum of the digits of a two digit number is 3.

• We subtract 9 from the number, the digits are inter changed

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Original number.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Original number = 21

$\large{\boxed{\boxed{\sf{Assumptions}}}}$

• Let n as the ten's digit of 2 digit number.

• Let m as the one's digit of 2 digit number.

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that the sum of the digits of a two digit number is 3. Afterwards it say us if we subtract 9 from the number, the digits are inter changed. Now it ask us to find the orignal number.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question firstly we have to make equation 1 and 2 afterthat finding the value of equation 1 and 2. Afterthat substituting the values we get our final result that is 21.

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

According to the question we already know that what is given or what to find. Let's see it again to understand it properly.

• The sum of the digits of a two digit number is 3 ( Given )

• We subtract 9 from the number, the digits are inter changed ( Given )

• Original number. ( To find )

According to question, let's carry on

➪ n + m ᴇǫᴜᴀᴛɪᴏɴ ❶ x + y

➪ Original number = 10n + m

➪ After interchanging the original number = 10m + n

Continuing.......

➪ 10n - n + m - 10m = 9

➪ 9n - 9m = 9

➪ 9(n-m) = 9

➪ n-m = 9/9

➪ n-m = 1 ᴇǫᴜᴀᴛɪᴏɴ ❷

Continuing... ᴇǫᴜᴀᴛɪᴏɴ ❶ from ᴇǫᴜᴀᴛɪᴏɴ ❷

➪ n + m - n + m = 3 - 1

Note : n and -n cut each other

➪ 2m = 2

➪ m = 2/2

➪ m = 1

Substituting the value of m as 1 in ᴇǫᴜᴀᴛɪᴏɴ ❶

➪ n + m = 3

➪ n + 1 = 3

➪ n = 3-1

➪ n = 2.

Now finding original number,

➪ 10n + m

➪ 10(2) + 1

➪ 20 + 1

➪ 21

Hence, original number will be 21

$\bold{\pink{\fbox{\pink{Answer 21}}}}$