Question

4. A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number
digits are reversed. Find the number.
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Answer 1

Answer:

Let the ten's place and one's place of the number be x and y respectively.

The number : 10x+y

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

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

6x-3y=3

3(2x-y)=

2x-y=1

y=2x-1 (i)

18+10x+y=10y+x

18+9x-9y=0

9y-9x=18

9(y-x)=18

y-x=2

2x-1-x=2

x=3

putting the value of x=3 in (i) , we get

y=2×3-1

y=5

The number is 10x+y

=10×3+5

=35

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