Given :
• (two-digit number) = 3 + 4(sum of its digits)
• (two-digit number) + 18 = Digit gets reverse
To Find :
• The number.
Concept :
-We will first assume the number on one's place be
and ten's place be
[why? because the given conditions are about the digits of number]
-Two-digit number then formed will be 10y + x and its reverse will be 10x + y[why? well let's take an example like a number 42. This number can be written in expanded form as 10×4+2×1 here 4 is number at ten's place (y) and 2 at one's place(x) It's reverse will be 24 it can be written in expanded form as 10×2+4×1 here 2 is number at ten's place (y) and 4 at one's place(x)]
-Then we will use given conditions to form the equation and will solve the equations to get the answer.
So now let's get started with our solution! :D
Solution :
Let the one's and ten's digit of the number be
and
respectively.
According to first condition,
=> (10y + x) = 3 + 4(x + y)
=> 10y + x = 3 + 4x + 4y
=> 10y - 4y = 3 + 4x - x
=> 6y = 3 + 3x
=> 2y - 1 = x ___(equation 1)
According to second condition,
=> (10y + x) + 18 = 10x + y
=> 10y - y + 18 = 10x - x
=> 9y + 18 = 9x
=> y + 2 = x ___(equation 2)
Solving equation 1 and 2
y + 2 = x (equation 2)
y + 2 = 2y - 1 [From equation 1]
3 = 2y - y
3 = y (ten's place)
Now put value of y = 3 in equation 2
y + 2 = x (equation 2)
3 + 2 = x
5 = x (one's place)
So, the number formed is 35.