# A number consists of two digits. When it is divided by the sum of its digits, the quotient is 6 with no remainder. When the number is diminished by 9, the digits are reversed. Find the number.

Let unit’s digit = y

and the ten’s digit = x

So, the original number = 10x + y

The sum of the number = 10x + y

The sum of the digit = x + y

According to the question, 10x + y = 6(x + y)

10x + y = 6x + 6y

10x + y – 6x – 6y

4x – 5y = 0 …(i)

The reverse of the number = x + 10y

and 10x + y – 9 = x + 10y

10x + y – 9 = x + 10y

10x – x + y – 10y = 9

9x – 9y = 9

x – y = 1

x = y + 1 …(ii)

On substituting the value of x = y + 1 in Eq. (i), we get

4x – 5y = 0

4(y + 1) – 5y = 0

4y + 4 – 5y = 0

4 – y = 0

y = 4

On substituting the value of y = 4 in Eq. (ii), we get

x = y + 1

x = 4 + 1

x = 5

So, the Original number = 10x + y

= 10×5 + 4

= 50 + 4

= 54

Hence, the two digit number is 54.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Pair of Linear Equations in Two Variables46 mins  Bonus on Applications of Linear Equations in Two Variables43 mins  Dealing With the Real Life Problems53 mins  HOT Topics of Applications of Linear Equations in Two Variables52 mins  NCERT I Quiz on Solution of Linear Equations in Two Variables49 mins  Learn to Solve Real Life Problems Using Linear Equations in Two Variables36 mins  Quiz | Solution of Linear Equations53 mins  Champ Quiz | Consistency and Inconsistency of Solutions36 mins  Dealing with the Real Life Problems54 mins  Smart Revision | Important Word Problems37 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 