A no. Consists of two digits whose sum is 7. If 45 is added to the no....
Problem Statement
A no. consists of two digits whose sum is 7. If 45 is added to the no. The digits are reversed find the number?
Solution
Let's assume that the two digits in the number are x and y.
Step 1: Forming the Equation
According to the problem statement, the sum of the digits is 7. Hence, we can form the equation:
x + y = 7 ... equation (1)
After adding 45 to the number, the digits are reversed. Hence, the new number can be formed as:
10y + x + 45
This number is also equal to:
10x + y
Forming an equation:
10y + x + 45 = 10x + y
9y - 9x = 45 - 45
9(y - x) = 0
y - x = 0 ... equation (2)
Step 2: Solving the Equations
We have two equations:
x + y = 7 ... equation (1)
y - x = 0 ... equation (2)
From equation (2), we get:
y = x
Substituting this value of y in equation (1), we get:
x + x = 7
2x = 7
x = 3.5
As x is not a whole number, this is not possible.
Step 3: Conclusion
Therefore, there is no number that satisfies the given conditions.