Question

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2. Sum of the digits of a 2-digit number is 10. The number obtained by interchanging the digits
exceeds the given number by 36. Find the given number.​

Answer 1

Answer:

Let the -

ten's digit be M

one's digit be N

Number = 10M + N

Sum of two digit number is 10.

=> M + N = 10

=> M = 10 - N ...(1)

The number obtained by interchanging the digits exceeds the original number by 36.

Interchanged number = 10N + M

=> 10N + M = 10M + N +36

=> 10N - N + M - 10M = 36

=> 9N - 9M = 36

=> N - M = 4

=> N - (10 - N) = 4 [From (1)]

=> N - 10 + N = 4

=> 2N = 14

=> N = 7

Substitute value of N in (1)

=> M = 10 - 7

=> M = 3

•°• Original number = 10M + N

=> 10(3) + 7

=> 30 + 7

=> 37

Answer 2

Answer:

The number is 37

Step-by-step explanation:

Let,

The units digit = x

The tens digit = 10 - x

Orignal Number :

⇒ 10 (10 - x) + x

⇒ 100 - 10x + x

⇒ 100 - 9x

★ Digit of the number interchange:

⇒ 10x + (10 - x)

⇒ 10x - x + 10

⇒ 9x + 10

★According to the question:

The number with reversed digits exceeds

the original number by 36 :

So,

⇒ (100 - 9x) + 36 = (9x + 10)

⇒ 100 + 36 - 9x = 9x + 10

⇒ 136 - 9x = 9x + 10

⇒ 136 - 10 = 9x + 9x

⇒ 126 = 18x

⇒ 18x = 126

⇒ x = 126 / 18

⇒ x = 7

The unit digit = 7

The tens digit = 10 - x

⇒ 10 - 7

⇒ 3

The tens digit = 3

Therefore,

The number is 37