Question

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A two digit number is 3 more than 4 times the sum of its digits.If 18 is added to the number its digit are reversed.Find the number

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Answer 1

Here is your answer

Let the tens digit of the number be y and ones digit of the number be x.

Remember

The two digit no.= 10x + y

On reversing the digits = 10y + x

Sum of digits = x + y

Now, according to the question - - >>

1st condition =>

10x + y = 4(x+y) +3

=>10x + y = 4x + 4y + 3

=> 6x - 3y =3

=>3(2x-y) = 3

=>2x - y =1 ----------((i))

2nd condition =>

10x + y +18 = 10y + x

=> 9x - 9y = - 18

=>9(x-y) = 9(-2)

=>x - y = - 2

=> y = 2+x -----------((ii))

Now, putting eq (ii) in (I), we get =>

(Solving the eq by substitution methord)

2x - (2+x) = 1

=>2x - 2 - x = 1

=>x = 3

And

y = 2+3 = 5

Hence the number is =>

10(3)+ 5

=>35

Thanks

Answer 2

8 answers · Mathematics

Best Answer

Let's say that the number looks like xy. Its value will be 10x + y.

It's "3 more than 4 times the sum of its digits" ... so:

10x + y = 4(x + y) + 3

10x + y = 4x + 4y + 3

10x - 4x - 3 = 4y - y

6x - 3 = 3y

2x - 1 = y …… (1)

"If 18 is added to the no. its digits are reversed" … so:

10x + y + 18 = 10y + x

10x - x + 18 = 10y - y

9x + 18 = 9y

x + 2 = y …… (2)

Equating (1) and (2):

2x - 1 = x + 2

2x - x = 2 + 1

x = 3

Into (2): y = 5

SOLUTION: The number is 35.

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Check:

• the sum of its digits = 8 …… 4 * 8 = 32 …… 32 + 3 = 35 (yes)

• 35 + 18 = 53 …… which is 35 with the digits reversed (yes)