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

# The sum of digits of a two-digit number is 13. If the difference between the number and the one obtained when the digits are interchanged is 45, find the number.

A
94
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
49
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
85
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
76
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is A 94 Let the digit in the units place be y and digit in the tens place be x. Then, the number is 10x+y and the number obtained on reversing the digits is 10y+x. From question, x+y=13 ...(1) 10x+y−(10y+x)=45 ⇒9x−9y=45 ⇒x−y=5 ....(2) On adding equations (1) and (2), we get 2x=18 ⇒x=9 On substituting x=9 in equation (1), we get 9+y=13 ⇒y=4 ∴The required number is 94.

Suggest Corrections
6
Join BYJU'S Learning Program
Related Videos
Algebraic Solution
MATHEMATICS
Watch in App
Join BYJU'S Learning Program