Question

a two digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, it's digits are reversed. Find the number.

Answer 1

Hii There!!!


Let two digits be 'x' and 'y' respectively


Thus, the two digit number is : 10x + y


Now,

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


(10x+y)+ 18=10y+x ------(ii)


Now, solving equation i)


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

=> 6x-3y=3

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

On Solving ii)

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

=> 9y-9x=18

=> y - x = 2 ------------2)



On adding eq. 1) and 2)

=> 2x-y+y-x=1+2

=> x=3

Thus, y=x+2 ---- from eq.2 )

=> y=5

Therefore the number will be = 10x+ y

=> 10 x 3 + 5 = 35



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Hope it helps ☺

Answer 2

Here is your solutions


Let ones place digit be x .

Tens place digit be y .

Original number = 10y + x

Number formed by reversing the digits = 10x + y

A two digit number is 3more than 4times the sum of its digits .

A/q

=>10y + x = 4(x + y) + 3 
=>10y + x − 4x − 4y = 3
 => 6y − 3x = 3 
=>2y − x = 1..................(1) 

Again when 18 is added to the number then digits get interchanged. 

(10y + x) + 18 = 10x + y 

=>9x − 9y = 18
=> x − y = 2...................(2) 

On adding equation (1) and (2):-

 2y − x +(x-y)= 1+2
2y-x+x-y = 3
Y = 3

Putting the value of y im equation (2)

=> x − y = 2
=>x- 3 =2
=>x= 2+3
=>x =5

Hence

Number = 10y +x= 10×3+5=35

Hope it helps you