A number consists of two digits whose sum is 9. If 27 is subtracted from the number it's digits are reversed. find the number? plss answer soon as possible
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A number consists of two digits whose sum is 9. If 27 is subtracted from the number it's digits are reversed. find the number? plss answer soon as possible
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Answer :
Explanation :
Given :
To find :
The number whose sum of digits is 9 and when 27 is subtracted from it , the digits of the number is reversed , Number = ?
Solution :
Let the digits of the two-digt number be a and b.
So,
Now,
According to the question , sum of digits of the two-digt number is 9 i.e,
⠀⠀⠀⠀⠀⠀⠀⠀⠀a + b = 9 ⠀⠀⠀⠀[Equation.(i)]
According to the question, when 27 is subtracted from the original number, the number is reversed i.e,
⠀⠀⠀⠀⠀⠀⠀⠀⠀(10a + b) - 27 = (10b + a)
By solving the above equation , we get :
==> (10a + b) - 27 = (10b + a)
==> (10a + b) - (10b + a) = 27
==> 10a + b - 10b - a = 27
==> 9a - 9b = 27
==> 9(a - b) = 27
==> a - b = 27/9
==> a - b = 3
∴ a - b = 3 ⠀⠀⠀⠀ [Equation.(ii)]
Now by adding Eq.(i) and Eq.(ii) , we get :
==> (a + b) + (a - b) = 9 + 3
==> (a + a) + (b - b) = 9 + 3
==> (a + a) + 0 = 9 + 3
==> (a + a) = 9 + 3
==> 2a = 12
==> a = 12/2
==> a = 6
∴ a = 6
Hence the value of a is 6.
Now by substituting the value of a in the Eq.(i) , we get :
==> a + b = 9
==> 6 + b = 9
==> b = 9 - 6
==> b = 3
∴ b = 3
Hence the value of b is 3.
By substituting the value of a and b in original number , we get :
==> 10a + b
==> (10 × 6) + 3
==> 60 + 3
==> 63
Therefore,
Verified answer
Answer:
63
Step-by-step explanation:
the answer is 63.
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