Question

The sum of digit of a two digit number is 10.if inter changing the digit,the new number is 18 more than the original number.what will be the original number?

Answer 1

i th8nk this might may help u first right let the number be x

Answer 2

Original Number = 64

Step-by-step explanation:

Given:

Sum of a two digit number is 10.

After interchanging digits the new number formed is 18 less than original.

To Find:

What is the original number ?

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

➟ Tens + Ones = 10

x + y = 10 or

x = (10 – y)......(1)

[ Now, interchanging the digits of the number ]

New number formed is 10y + x

A/q

After interchanging digits the new number formed is 18 less than original.

$\implies{\rm }$⟹ 10x + y = 10y + x – 18

$\implies{\rm }$⟹ 10x – x = 10y – y – 18

$\implies{\rm }$⟹ 9x = 9y – 18

$\implies{\rm }$⟹ 9x – 9y = – 18

$\implies{\rm }$⟹ 9(x – y) = – 18

$\implies{\rm }$⟹ x – y = 2

$\implies{\rm }$⟹ (10 – y) – y = 2

$\implies{\rm }$⟹ – 2y = 2 – 10

$\implies{\rm }$⟹ – 2y = – 8

$\implies{\rm }$⟹ y = 8/2 = 4

So, the digits of number is

• Ones digit is y = 4

• Tens digit is x = 10 – 4 = 6

Hence, the original number is 10(6) + 4 = 64