Question

Sum
digits of
two digit
number is 7. When we interchange the
digit, it is found that the resus
number is quäler
original number by 27. What is the
number
than the
atroo digit​

Answer 1

Answer:

27

Sum

digits of

two digit

number is 7. When we interchange the

digit, it is found that the resus

number is quäler

original number by 27. What is the

number

than the

atroo digit

Answer 2

Answer:



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Ncert solutions

Grade 8

Mathematics

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Chapters in NCERT Solutions - Mathematics , Class 8



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=18108=6

Hence, the 2-digit number = 10(9-x)+x = 10(9-6)+6 = 10 x 3 + 6 = 30 + 6 = 36