Question

The sum of the digits of a two digit number is 15. If the number formed by reversing the digits is less than the original number by 27 thenn find the original number​

Answer 1

Original Number = 96

Step-by-step explanation:

Given:

• Sum of digits of two digit number is 15.
• Reversed number is 27 less than original.

To Find:

• What is the original number ?

Solution: Let the tens digit be x and ones digit be y. Therefore original number is 10x + y.

Tens + ones = 15

x + y = 15

x = (15 – y)......1

[ Now reversing the digits new number formed will be ]

• Reversed number = 10y + x

A/q

Reversed number is 27 less than original number.

$\implies{\rm }$ 10x + y – 27 = 10y + x

$\implies{\rm }$ 10x – x – 27 = 10y – y

$\implies{\rm }$ 9x – 27 = 9y

$\implies{\rm }$ 9(x – 3) = 9y

$\implies{\rm }$ x – 3 = 9y/9

$\implies{\rm }$ 15 – y – 3 = y

$\implies{\rm }$ 12 = y + y

$\implies{\rm }$ 12 = 2y

$\implies{\rm }$ 6 = y

So the digits of number is

Ones digit is y = 6

Tens digit is x = 15 – 6 = 9

∴ Number is 10(9) + 6 = 90 + 6 = 96

Answer 2

⚘ Given :-

• The sum of the digits of a two digit number is 15.

• The number formed by reversing the digits is less than the original number by 27.

⚘ To Find :-

• The Original Number.

⚘ Solution :-

Let,

Ones Digit be x.

Tens Digit be y.

So, Original Number = 10x + y.

Now, It is Given,

➛x + y = 15.

➛x = 15 - y.

Now, Reversed Number = 10y + x.

According To The Question, The Equation :-

➛10x + y - 27 = 10y + x.

➛10x - x - y - 10y = 27.

➛9x - 27 = 9y.

➛9(x - 3) = 9y.

➛x - 3 = 9y/9.

➛x - 3 = y.

➛15 - y - 3 = y

➛2y = 12.

➛y = 6.

So,

• Ten's Digit = x = 6.

• One's Digit = 15 - y = 9.

Hence, The Number Formed = 96.