Question : By interchanging the digits of a two-digit number, we get a number which is four times the original number minus 24. If the digit at the unit's place of the original number exceeds its digit at ten's place by 7, then the original number is:
Option 1: 29
Option 2: 36
Option 3: 58
Option 4: 18
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: 29
Solution :
Let the digit in the ten's place and the digit in the unit's place be x and y respectively.
Then the original number = 10x + y and the new number = 10y + x.
According to the question,
10y + x = 4(10x + y) – 24
or, 10y + x = 40x + 4y– 24
or, 39x – 6y = 24
or, 13x – 2y = 8 -------------------------------(1)
Also, given that y – x = 7
so, y = x + 7 -----------------------------------(2)
Now, putting the value of y in (1)
13x – 2(x + 7) = 8
or, 13x – 2x – 14 = 8
or, 11x = 22
or, x = 2
Now, from (2) we get,
y = 2 + 7
or, y = 9
Putting the value of x and y in the original number, we get,
10x + y = (10 × 2) + 9 = 29
Hence, the correct answer is 29.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
