# when you reverse the digits of the number 13, the number increases by 18. how many other twodigit numbers increase by 18 when their digits are reversed?

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Guys, does anyone know the answer?

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## When you reverse the digits of the number 13 , the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

When you reverse the digits of the number 13 , the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

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When you reverse the digits of the number 13 , the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

Question

When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by 18 when their digits are reversed?

___ Open in App Solution

Let 10x + y be a two digit number, where x and y are positive single digit integers and

x > 0 .

Its reverse = 10y + x

Now, 10y + x - 10x - y = 18

∴ 9(y - x) = 18 ∴ y - x = 2

Thus y and x can be (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8) and (7, 9)

∴

Other than 13, there are 6 such numbers.

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## When you reverse the digits of the number 13, the number increases by 18

## When you reverse the digits of the number 13, the number increases by 18

Numbers

When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

5 6 7 8

**Answer**

Let the two-digit number be ab.

When the digits are reveres (ba), the number is increased by 18.

(10a+b) - (10b+a) = 18

a - b = 2

All such numbers that have unit's digit greater than ten's digit by 2.

Numbers are (except 13) 24, 35, 46, 57, 68, 79. So. there are 6 other numbers.

**The correct option is B.**

## When you reverse the digits of the number 13, the number increases by 18. How many other 2 digit numbers increase by 18 when their digits are reverse?

Answer (1 of 11): This can be calculated easily. As any two digit number can be written in the following form: N= 10x +y If we reverse the number now, it would become: N' = 10y + x So if we subtract one from the other, we should obtain 18 ( as mentioned in the question ). N-N'= 18 => x-y ...

When you reverse the digits of the number 13, the number increases by 18. How many other 2 digit numbers increase by 18 when their digits are reverse?

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Praveenkumar Kalikeri

Engineer by Choice, Maths Educator by passionAuthor has 1.1K answers and 2.2M answer views4y

Thanks A2A.

Assume the number to be N= 10a + b

If the digits of the number are interchanged, then we have N' = 10b + a

It is also given that the difference between the number & reversed number is 18.

N' = N + 18

10b + a - 10a - b = 18

9b - 9a = 18 b - a = 2

Therefore, the values a & b can take are as follows.

b = 9, 8, 7, 6, 5, 4, 3, 2

a = 7, 6, 5, 4, 3, 2, 1, 0

Therefore, the numbers are 02, 13, 24, 35, 46, 57, 68, 79.

Hope this helps you.

Sai Sudharshan

Architect | Designer | Artist6y

An equation in 2 variables can be obtained for this.

Assume that the digits of the 2 digit number are 'x' and 'y'.

The 2 digit number is represented as: 10x + y [In the example you have given, x=1 and y=3, therefore, it can be represented as 10(1) + 3 = 13]

It is also given that on adding 18 to the given number, the digits are reversed. Representing that in the form of a linear equation:

10x + y + 18 = 10y + x [RHS = Digits are reversed]

9x - 9y = -18 x - y = -2 => y - x = 2

Substitute values for x and y such that the above equation is satisfied.

On substituting values for x and y, we get the followin

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Kanishk Chauhan

PhD Physics, Ohio University, USA6y

This can be calculated easily.

As any two digit number can be written in the following form:

N= 10x +y

If we reverse the number now, it would become:

N' = 10y + x

So if we subtract one from the other, we should obtain 18 ( as mentioned in the question ).

N-N'= 18 => x-y = 2

Thus, any number whose digits differ by two would be an aswer to the question.

The only numbers which satisfy this are : 13,24,35,46,57,68,79

But this would not be true for any 3 or more digit number.

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Mahesh Reddy

Author has 1.5K answers and 1.8M answer views6y

Let ab is the number where a is in tens place , B is in unit place . so

Value of a= 10 × a b=1×b

Value of total number = 10a+b

After shifting the digits , the number would be ba

So value of ba =10b+a

10b+a -(10a+b)= 18

So after simplification

b-a =2

So for every number if the unit digit is greater than tens digit by 2 , then the reverse of digits will give the resultant number 18 greater than the original number .

13,24,35,46,57,68,79

Diane Chen

Hardware Design Engineer, Consumer Electronics6y

Assume this 2 digit number is ab, then we will get the following equation:

10*a+b+18=10*b+a we get: a-b=2

so the numbers are: 13, 24, 35, 46, 57, 68, 79

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Rohit Ranjan

Studied at Biju Patnaik University of Technology (Graduated 2017)4y

Let the two-digit number be ab.

When the digits are reveres (ba), the number is increased by 18.

(10a+b) - (10b+a) = 18

a - b = 2

All such numbers that have unit's digit greater than ten's digit by 2.

Numbers are (except 13) 24, 35, 46, 57, 68, 79. So. there are 6 other numbers

Sankhya

Technical Consulting Engineer [IOS-XR] at Cisco (company) (2019–present)Author has 58 answers and 43.6K answer views3y

Related

The sum of a particular two-digit number is 14. If this number's digits are reversed, the number is increased by 18. What is this number?

Let the digit in units place be y

Let the digit in ten's place be x

So the number is 10x+y

After reversing the places of the digits the number is 10y+x

The relationship between the actual number and after reversing is :

10x+y+18= 10y+x 9x-9y=-18

y-x=2 ………….. Equation 1

Again,

x+y=14 ………… Equation 2

Adding the two equations :

X is cancelled out and y=8

Substituting value of y in any of the two equations we get x=6

So the number is 68

If you reverse the digits it becomes 86 , which is 18 greater than the number

Guys, does anyone know the answer?