- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
Given :
A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed.
To find :
We have to find the number.
Solution :
Let the number be $10x+y$.
According to the question,
$10x+y=4(x+y)$
$10x+y=4x+4y$
$10x-4x=4y-y$
$6x=3y$
$2x=y$....(i)
It is also given that if 18 is added to the number the digits gets reversed.
Therefore,
$10x+y+18 = 10y+x$
$10y+x-10x-y = 18$
$10y-y+x-10x= 18$
$9y-x(10-1)=18$
$9y-9x=18$
$9(y-x)=18$
$y-x=\frac{18}{9}$
$y-x=2$
$2x-x=2$ (From (i))
$x=2$
This implies,
$y=2x=2(2)=4$
The original number is $10(2)+4=20+4=24$.
Therefore, the number is 24.
Advertisements