Sun of the digits of a two digit number is 9 when we interchange the digits it is found that the ruselting new number is greater then the orginal number by 27 what is the two digit number
Answers
Let ten's digit number be M and one's digit number be N.
Sum of two digits of a number is 9.
According to question
⇒ M + N = 9
⇒ M = 9 - N ___ (eq 1)
On interchanging number, the new number is greater than the original number by 27.
Original number = 10M + N
Interchanged number = 10N + M
According to question
⇒ 10N + M = 10M + N + 27
⇒ 10N - N + M - 10M = 27
⇒ 9N - 9M = 27
⇒ N - M = 3
⇒ N - (9 - N) = 3 [From (eq 1)]
⇒ N - 9 + N = 3
⇒ 2N = 12
⇒ N = 6
Substitute N = 6 in (eq 1)
⇒ M = 9 - 6
⇒ M = 3
∴ Original number = 10M + N
From above calculations M = 3 and N = 6
So,
⇒ 10(3) + 6
⇒ 30 + 6
⇒ 36
•°• Two digit number is 36.
Answer :
36
Step-by-step explanation:
Sum of the digits of a 2 digit no. = 9
As we know,
we can write any 2 digit no. in the form of 10x + y.
So,
Let the unit digit be x and the tens digit be y.
here,
10x + y _____Original no.
10y + x _____Reversed no.
x + y = 9 . . . [ eq.i ]
Than y = 9 - x . . . [ eq.ii ]
Solution :
10y + x = ( 10x + y ) + 27
10(9-x) + x = 10x + 9-x + 27
90 - 10x + x = 9x + 36
90 - 36 = 9x + 9x
54 = 18x
3 = x
(X) The unit digit is 3
And the tens digit (Y) 9-3 = 6
Verification :
Reversed no. = Original no.+ 27
63 = 36 + 27
L.H.S = R.H.S
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