Question

3) sum of digits of two -digit number is
9. When we interchange the digits, it is
found that resulting new number is greater
than the original number by 27. What is
the two-digit number​

Answer 1

Answer:

$\large{\underline{\boxed{\sf Original \: number =36}}}$

Step-by-step explanation:

Let the unit's digit of a two-digit number be y and ten's digit be x.

∴ Original number = 10y + x

According to the question ;

⇒ 10x + y = 10y + x + 27

⇒ 10x - x + y - 10y = 27

⇒ 9x - 9y = 27

⇒ 9(x - y) = 27

⇒ x - y = $\sf \dfrac{27}{9}$

⇒ x - y = 3.... (i)

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Also, it is given that -

Sum of numbers = 9

⇒ x + y = 9.... (ii)

On adding equation (i) and (ii) -

⇒ x - y + x + y = 3 + 9

⇒ 2x = 12

⇒ x = $\sf \dfrac{12}{2}$

⇒ x = 6

Putting the value of x in (i) -

⇒ x - y = 3

⇒ 6 - y = 3

⇒ y = 6 - 3

⇒ y = 3

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Therefore,

⇒ Number = 10y + x

⇒ Number = 10 * 3 + 6

⇒ Number = 36

Hence, the required number is 36.

Answer 2

• Let ten's digit be M and one's digit be N

» Original number = 10M + N

• Sum of digits of two -digit number (i.e. M and N) is 9.

=> M + N = 9

=> M = 9 - N ________(eq 1)

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• When we interchange the digits, it is

found that resulting new number is greater than the original number by 27.

After interchanging the new digit is 10N + M

=> 10N + M = 10M + N + 27

=> 10N - N + M - 10M = 27

=> 9N - 9M = 27

=> N - M = 3 ________ (eq 2)

=> N - (9 - N) = 3

=> N - 9 + N = 3

=> 2N = 12

=> N = 6

• Put value of N in (eq 1)

=> M = 9 - 6

=> M = 3

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We have to find two digit number

• Original number = 10M + N

=> 10 × 3 + 6

=> 36

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The two digit number is 36

__________ [ANSWER]