1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# In a two-digit number, the digit at tens place is double the digit at units place. If the digits of the number are interchanged, the new number so formed is 27 less than the original number. Find the original number.

A
55
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
60
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
63
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
68
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is C 63Let, the digit at tens place be x and the digit at units place be y in the original number.Then the original number =10+y, and the new number obtained by interchanging the digits =10y+x.By the data, the digit at tens place is double the digit at units place.∴x=2y∴x−2y=0 ............. (1)Again, new number = original number - 27∴10y+x=10x+y−27∴10y+x−10x−y=−27∴−9x+9y=−27 ∴x−y=3 ........... (2)Subtracting eq. (1) from eq. (2),x−y=3x−2y=0- + -__________ y=3Substituting y=3 in x−2y=0∴x−2(3)=0∴x−6=0∴x=6Then, the original number =10x+y=10(6)+3=63Hence, the original number is 63.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Expression formation
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program