Question
The sum of the digits of a two-digit number is 7. If the number formed by interchanging the digits is less than the original number by 27, then find the original number.
Answer: Option C
:
C
Given, the sum of the digits of a two-digit number is 7.
Let the units digit of theoriginal number bex.
Then, the tens digit of theoriginal number is7−x.
The two-digit number=10(7−x)+(1×x)
=70−10x+x=70−9x
When the digits are interchanged,the new number is10(x)+1(7−x)=10x−x+7=9x+7
New number = Original number - 27
9x+7=70−9x−2718x=36x=2
The tens digit=7−x=7−2=5
∴The original number is 52.
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:
C
Given, the sum of the digits of a two-digit number is 7.
Let the units digit of theoriginal number bex.
Then, the tens digit of theoriginal number is7−x.
The two-digit number=10(7−x)+(1×x)
=70−10x+x=70−9x
When the digits are interchanged,the new number is10(x)+1(7−x)=10x−x+7=9x+7
New number = Original number - 27
9x+7=70−9x−2718x=36x=2
The tens digit=7−x=7−2=5
∴The original number is 52.
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