A number consists of two digits whose sum is 9,when 27 is added to this number,the digits interchange their places. The number is.…………
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Answer:
SOLUTION ::
Let unit place = b, ten place = a
So the number is 10a+b
Now by the given condition
a+b= 9 - - - - - - - - (1)
when number’s digits are reversed then resulting number is 10b + a
Since the number formed by reversing the digits is less than the original number by 9
(10b + a ) - ( 10a +b ) = 27
➙ 9a - 9b = - 27
➙ a - b = - 3 - - - - - - - (2)
Adding Equation (1) & Equation (2)
2a = 6
➙ a = 3
From Equation (1)
b = 9 - 3 = 6
So the original number is = (10×3) + 6 = 36
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Answer:
The number is 36
Step-by-step explanation:
Let,
Units digit = x
Tens digit = 9 - x
The sum of 2 digit = 9
Original number :
⇒ 10 (9 - x) + x
⇒ 90 - 10x + x
⇒ 90 - 9x
The digits are interchanged:
⇒ 10x + (9 - X)
⇒ 10x - x + 9
⇒ 9x + 9
★ According to the question:
Original number when added by 27 gives the number with reverse digit
⇒ (90 - 9x) + 27 = (9x + 9)
⇒ 90 + 27 - 9x = 9x + 9
⇒ 117 - 9x = 9x + 9
⇒ 117 - 9 = 9x + 9x
⇒ 108 = 18x
⇒ 18x = 108
⇒ x = 108 / 18
⇒ x = 6
Units digit = 6
Tens digit = 9 - x
⇒ 9 - 6
⇒ 3
Tens digit = 3
Therefore,
The number is 36