Question

sum of digit of a two digits number is 10 when the digits are inter changed the new number is 18less than the orginial number what is the number​

Answer 1

Answer:

Now, sum of digits is 10. Therefore, x+y=10. And interchanging the digits, it's increased by 10. Hence, 10x + y = 10y + x + 18.

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