Question

The sum of the digits of a given two digit number is 5. If the digit are reversed the new number is reduced by 27. Find the given number​

Answer 1

Answer:

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Answer 2

Given:

The sum of the digits of a given two digit number is 5.If the digit are reversed the new number is reduced by 27.

To find:

The given number

Solution:

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

Given that x + y = 5......(1)

According to the question

10x + y = 5

after reversed the number will be 10y + x

Given, Original number - reversed number = 27

(10x + y) - (10y + x) = 27

10x - x + y - 10y = 27

9x - 9y = 27

Now, 9x = 27 or 9y = 27

x = 27/9 or y = 27/9

x = 3 or y = 3

Now, in the equation,

x - y = 3.........(2)

Also from (1), y = 5 - x....(3)

Substitute (3) in (2) to get x-(5-x) = 3

x - 5 + x = 3

2x = 3 + 5

2x = 8

x = 4 ( by dividing)

Substitute x = 4 in (3)

y = 5 - 4 (substituting x value)

y = 1