- Trending Categories
- 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.

- Related Articles
- A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
- A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.
- A number has two digit whose sum is 9.If 27 is added to the number its digits are reversed. Find the number.
- The sum of digits of a two-digit number is 8. If 36 is added to the number then the digits reversed. Find the number.
- A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.
- The sum of the digits of a 2-digit number is 8. If the digits are reversed, the new number increases by 18. Find the number.
- A two-digit number is 4 times the sum of its digits and twice the product of the digits. Find the number.
- A two-digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.
- A number consists of two digit whose sum is $9$. If the digits are reversed, the new number is $\frac{3}{8}$ of the number. Find the number.
- The digits of a two-digit number differ by 3. If the digits are interchanged and the resulting number is added to the original number, the sum is 143. What is the original number?
- The units digit of a two digit number is 3 and seven times the sum of the digits is the number itself. Find the number.
- A number consists of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.
- The difference of the digits of a two-digit number is 2. The sum of that two-digit number and the number obtained by interchanging the places of its digits is 132. Find the two-digit number(s).
- Seven times a two-digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3. Find the number.
- A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number.

Advertisements