Question

(m) The sum of the digits of a two-digit number is 9. Also, nine times this number is
twice the number obtained by reversing the order of the digits. Find the number.
​

Answer 1

Given :

• The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits.

To Find :

• The Original Number = ?

Solution :

Let unit digit number be m and ten's digit number be n

• Original Number = 10m + n

• Number after reversing the digit = 10n + m

★According to Question now :

⊷ m + n= 9 .....[Equation (i)]

⊷ 9(10m + n) = 2(10n + m)

⊷ 90m + 9n = 20n + 2m

Combining like terms :

⊷ 90m - 2m = 20n - 9n

⊷ 88m = 11n

Dividing both the sides by 11 :

⊷ 8m = n .......[Equation (ii)]

Now, substitute the value of n from equation (ii) to equation (i) :

→ m + n = 9

→ m + 8m = 9

→ 9m = 9

Dividing both the sides by 9 we get :

→ m = 1

Now, subsitute the value of m in equation (ii) :

➻ 8m = n

➻ 8(1) = n

➻ 8 = n

➻ n = 8

Therefore,

• Original Number = 10m + n = 10(1) + 8 = 10 + 8 = 18

Answer 2

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

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

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

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

• The sum of the digits of a two-digit number is 9.
• Also, nine times this number is twice the number obtained by reversing the order of the digits.

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

• What is original number ?

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

• The original number is 18

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

$\implies$ $\large\purple{\texttt{Let unit digit of number be x}}$

$\implies$ $\large\purple{\texttt{Let ten's digit of number be y}}$

✪ Original number be 10x + y

✪ Number after reversing the digits be 10y

+x

$\large\gray{\texttt{Now let's carry on}}$

$\large\gray{\texttt{According to the Question}}$

✯ x + y = 9 $\large\red{\texttt{Equation 1}}$

✯ 9(10x + y) = 2(10y + x)

✯ 90x + 9y = 20y + 2x

$\large\gray{\texttt{Now we combining like terms}}$

✯ 90x - 2x = 20y - 9y

✯ 88x = 11y

✯ 11x = y $\large\red{\texttt{Equation 2}}$

$\large\purple{\texttt{Substituting the value we get -}}$

✯ x + y = 9

✯ x + 8x = 9

✯ 9x = 9

✯ m = 1

$\large\purple{\texttt{Substituting the value we get -}}$

✯ 8x = y

✯ 8(1) = y

✯ 8 = y

✯ y = 8

Therefore, the original number =>

10x + y = 10(1) + 8 = 10 + 8 = 18

$\huge{\boxed{\sf{18 \: is \: Answer}}}$

More to know !

What are like terms in algebraic expressions ?

In algebra, like terms are terms that have the same variables and powers

What is term in algebraic expressions ?

A term is a single mathematical expression. It may be a single number (positive or negative), a single variable ( a letter ), several variables multiplied but never added or subtracted.

@Itzbeautyqueen23

Hope it's helpful