Question

the sum of the digital of a 2-digit number is 6.on reversing it's digits,the number is 18 less than the original number. Find the number ​

Answer 1

Answer:

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Given:-

• The Sum of the Digit of a Two Digit number is 6.
• On reversing, the number is 18 less than the original number.

To Find:-

• The original Number.

Solution :-

Let the Ones digit be "x"

Ten's digit be = (6 - x)

Original Number :

➙ x + 10(6 - x)

➙ x + 60 - 10x

➙ 60 - 9x

According to the question or ATQ :

One's Digit = (6 - x)

One's Digit = (6 - x)Ten's digit = x

New Number :

➙10 × x + (6 - x)

➙ 9x + 6.

So,

➨ (New Number) - (Original Number) = 18

➨ (9x + 6 ) - (60- 9x) = 18

➨ 9x + 6 - 60 + 9x = 18

➨ 18x - 54 = 18

➨ 18x = 18 + 54.

➨ 18x = 72

➨ x = 72/18

➨ x = 4.

Therefore,

➸ One's Digit = x = 4

➸ Ten's digit = 6 - x = 2

Original Number = 42

Henceforth, the original number is 42.

Answer 2

Let the Ones digit be "x"

ten's digit be = (6 - x)

Original Number = x + 10(6 - x) = 60 - 9x

Now, Atq.

One's Digit = (6 - x)

Ten's digit = x

New Number = 10 × x + (6 - x) = 9x + 6.

So,

(New Number) - (Original Number) = 18

(9x + 6 ) - (60- 9x) = 18

9x + 6 - 60 + 9x = 18

18x - 54 = 18

18x = 18 + 54.

18x = 72

x = 72/18

x = 4.

Therefore,

One's Digit = x = 4

Ten's digit = 6 - x = 2

Original Number = 42

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