Question

The sum of the digits of a two-digit number is 10, while when the digits are reversed, the number decreases by 54. Find the changed number.

Answer 1

Answer:

82

Step-by-step explanation:

Let the ten's place digit be x and one's place digit be y

We know that a two digit number is of form

10×Ten Place Digit + One Place Digit

∴ Our Original number = 10x + y

and number made by reversing the digits = 10y + x

Now, given that

Sum of digits = 10

∴ x + y = 10

or x = 10 - y -------- ( i )

According to Question

number formed by reversing the digits = Original Number - 54

∴ 10y + x = 10x + y - 54

9y - 9x = -54

Dividing both sides by 9

y - x = - 6

Putting value of x from ( i )

y - (10 - y) = - 6

y + y - 10 = -6

2y = 4

y = 2

Putting value of y in ( i )

x = 10 - y

x = 10 - 2

x = 8

∴ number = 10x + y

                = 10×8 + 2

                = 82

Desired Number is 82

Check : Sum of digits: 8+2 = 10

Also 28 = 82 - 54 [ Reversed number is 54 less than original one ]

Answer 2

Step-by-step explanation:

The answer is done in the above picture.

Hope it helps