Question

a two digit number is 3 more than 4 times the sum of its digit if 18 is added to the number its digits are reserved find the number

Answer 1

For ones place we take ( x) and for tens (y)
Original number = 10y + x
Number formed by reversing the digits = 10x + y
Given 10y + x = 4(x + y) + 3
⇒ 10y + x − 4x − 4y = 3
⇒ 6y  − 3x  = 3
⇒ 2y  − x  = 1 → (1)
Also given that when 18 is added to the number the digits gets interchanged.
Hence (10y + x) + 18 = 10x + y
⇒ 9x − 9y = 18
⇒ x − y = 2  → (2)
Add (1) and (2), we get
2y  − x  = 1
x − y = 2
---------------
y = 3
Put y=3 in x − y = 2, we get
x − 3 = 2
∴ x = 5
Hence (10y + x) = 10(3) + 5 = 35

Answer 2

Hi.

Here is your answer---

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Let the unit digit in two digit number be y and Tens digit be x

Thus, Number = 10x + y 
 
According to the Question---

                             10x + y = 3 + 4( x + y) 
                             10x + y = 3 + 4x + 4y
                             10x - 4x + y - 4y = 3 
                                6x - 3y = 3          ------------------------eq(i)

Also,   10x + y +18 = 10y + x
           10x - x + y - 10y = -18
                9x - 9y = -18
                   x - y =  -2 
                    x = y - 2 ------------------------------------------eq(2)

Putting the eq(i) in the eq(2)

                      6(y - 2) - 3y = 3
                      6y - 12 - 3y = 3
                         3y -12 = 3
                            3y = 15
                             y = 5

Putting y =5 in eq(ii)
    
        x = 5 - 2
         x  = 3
Thus, Number  = 10x + y
                        = 10(3) + 5
                        = 30 + 5
                        = 35

Thus, two-digit number is 35.

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