Question

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.
(CBSE 20010]​

Answer 1

Let the digit at once place be x

Let the digit at tens place be y

Hence, Number = ( 10×y ) + x

According to question

( 10×y ) + x = 4 × ( x + y ) + 3

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

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

-3x + 6y = 3

3x - 6y = -3

x -2y = -1 – ( 1 )

Now reversed digit number = 10x + y

10y + x + 18 = 10x + y

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

-9x + 9y = -18

-x + y = -2 – ( 2 )

Adiing 1 & 2 we get

x – x – 2y + y = – 1 – 2

– y = – 3

y = 3

Put y = 3 in ( 1 )

x – 2 ( 3 ) = – 1

x – 6 = – 1

x = – 1 + 6

x = 5

Hence, Number is = 10y + x = 30 + 5 = 35

Hope the solution is clear to you.