a number consists of 2 digits whose sum is 8,if 18 is added to the number its digits are reversed ,find the number?
35 + 18 = 53
To find the number, let's assume the digits of the number as A and B.
According to the given information, the sum of the digits is 8. Therefore, we can write the equation:
A + B = 8 ---(Equation 1)
Now, it is also mentioned that if 18 is added to the number, its digits are reversed. This means if we add 18 to AB, it should be equal to BA.
So, we can write the equation:
10A + B + 18 = 10B + A ---(Equation 2)
Now, let's solve these equations and find the values of A and B.
From Equation 1, we have A = 8 - B.
Substituting this value of A in Equation 2, we get:
10(8 - B) + B + 18 = 10B + (8 - B)
Simplifying this equation, we get:
80 - 10B + B + 18 = 10B + 8 - B
Combining like terms, we have:
-9B + 98 = 9B + 8
Bringing like terms together, we get:
-9B - 9B = 8 - 98
-18B = -90
Dividing both sides of the equation by -18, we get:
B = 5
Now we can substitute the value of B in Equation 1 to find the value of A:
A + 5 = 8
A = 8 - 5
A = 3
So, the two-digit number where the sum of the digits is 8 and when 18 is added to the number its digits are reversed is 35.