If the sum of digits of
a two-digit number is greater than 9, then the product of the digits of the number will always be greater than
Answers
Step-by-step explanation:
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Grade 8
Mathematics
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Chapters in NCERT Solutions - Mathematics , Class 8
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Exercises in Linear Equations in One Variable
Question 3
Q3) Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
Solution
Transcript
Solution:
Let the unit place digit of a two-digit number be x.
Therefore, the tens place digit = 9-x
\because∵ 2-digit number = 10 x tens place digit + unit place digit
\therefore∴ Original number = 10(9-x)+x
According to the question, New number
= Original number + 27
\Rightarrow10x+\left(9-x\right)=10\left(9-x\right)+x+27⇒10x+(9−x)=10(9−x)+x+27
\Rightarrow10+9-x=90-10x+x+27⇒10+9−x=90−10x+x+27
\Rightarrow9x+9=117-9x⇒9x+9=117−9x
\Rightarrow9x+9x=117-9⇒9x+9x=117−9
\Rightarrow18x=108⇒18x=108
\Rightarrow x=\frac{108}{18}=6⇒x=
18
108
=6
Hence, the 2-digit number = 10(9-x)+x = 10(9-6)+6 = 10 x 3 + 6 = 30 + 6 = 36
Answer:
100 must be your correct answer