10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

The sum of the digits of a two digit number is 9. If 27 is added to the number, its digits reverse. The number is: (NCERT EXEMPLAR)

A) 25

B) 72

C) 63

D) 36

Correct Answer: D

Solution :

[d] Let unit digit and ten's digit are y and x respectively.

By condition, \[x+y=9\] ...(1)

and \[(10x+y)+27=10y+x\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,9y-9x=27\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,y-x=3\] .(2)

From eqs. (1) and (2), we get

\[y=6\] and \[x=3\]

\[\therefore \]Required number \[=10\times 3+6=30+6=36\]