Question

The sum of the digits of a two digit number is 11. If the tens digit is 5 less than the ones digit. Find the number

Answer 1

GIVEN:

• The sum of the digits of a two digit number is 11.
• If the tens digit is 5 less than the ones digit.

TO FIND:

• What is the number ?

SOLUTION:

Let the digit at ten's place be 'x' and the digit at unit's place be 'y'

• NUMBER = 10x + y

CASE:- 1)

✧ The sum of the digits of a two digit number is 11.

According to question:-

➲ x + y = 11....❶

CASE:- 2)

✧ If the tens digit is 5 less than the ones digit.

According to question:-

➲ x = y –5....❷

Put the value of 'x' from equation 2) in equation 1)

➲ y –5 +y = 11

➲ 2y = 11 + 5

➲ 2y = 16

➲ y = $\sf{\cancel\dfrac{16}{2}}$

【y = 8】

Put the value of 'y' in equation 2)

➲ x = 8 –5

【x = 3】

• NUMBER = 10(3) + 8
• NUMBER = 30 + 8
• NUMBER = 38

❝ Hence, the number formed is 38 ❞

______________________

Answer 2

Question -

The sum of the digits of a two digit number is 11. If the tens digit is 5 less than the ones digit. Find the number.

Given - Sum of two digit number =11

And, tens digit is 5 less than the ones digit.

To find :- Find the number.

Answer -

Let the ones number be x and tens number be y.

Then, x+y= 11.......... (1)

And, x= y-5........... (2)

Now, putting the value of equation(2) in equation (1), we get

$\rm{y - 5 + y = 11}$

$\implies \: 2y - 5 = 11$

$\implies \: 2y = 11 + 5 \:$

$\implies \: 2y = 16$

$y = \sf{\cancel\dfrac{16}{2}} = 8</p><p>$

Putting y=16 in equation (1), we get

8+ x =11

$\implies \: x = 11 - 8 = 3$

Hence, the number is 38.