Question

In a two digit number the sum of the digits is nine. If the number is reversed then the new number is 9 less than 3 times the original number find the original number with explanation
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Answer 1

Step-by-step explanation:

Let the -

• ten's digit number be "M"
• one's digit number be "N"

In a two digit number the sum of the digits is nine.

According to question,

→ M + N = 9

→ M = 9 - N ___ (eq 1)

If the number is reversed then the new number is 9 less than 3 times the original number.

• Original number = 10M + N
• Revered number = 10N + M

According to question,

→ 10N + M = 3(10M + N) - 9

→ 10N + M = 30M + 3N - 9

→ 10N - 3N + M - 30M = - 9

→ 7N - 29M = - 9

→ 7N - 29(9 - N) = - 9

→ 7N - 261 + 29N = - 9

→ 36N = - 9 + 261

→ 36N = 252

→ N = 7

(One's digit = 7)

Substitute value of N in (eq 1)

→ M = 9 - 7

→ M = 2

(Ten's digit = 2)

So,

Original number = 10M + N

→ 10(2) + 7

→ 20 + 7

→ 27

∴ Original number is 27.

Answer 2

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