A number when reversed become 45% greater than the original. By how mu...
Solution:
Let's assume the original number to be "ab", where 'a' represents the tens place digit and 'b' represents the units place digit.
According to the given condition, when the number is reversed, it becomes "ba" and it is 45% greater than the original number.
Step 1: Calculate the Reversed Number
The reversed number is obtained by interchanging the digits 'a' and 'b'. Therefore, the reversed number is "ba".
Step 2: Express 45% as a Decimal
To calculate the percentage increase, we need to express 45% as a decimal.
45% = 45/100 = 0.45
Step 3: Form the Equation
Since the reversed number is 45% greater than the original number, we can form the equation as:
ba = ab + 0.45 * ab
Simplifying the equation, we get:
ba = ab * (1 + 0.45)
Step 4: Substitute the Variables
Substituting 'a' and 'b' with their respective values, we get:
10a + b = 10b + a * (1 + 0.45)
Simplifying further, we have:
10a + b = 10b + 1.45a
Step 5: Solve the Equation
Now, we can solve the equation to determine the relationship between the units place digit and the tens place digit.
10a - 1.45a = 10b - b
8.55a = 9b
Step 6: Calculate the Percentage Difference
To calculate the percentage difference between the units place digit and the tens place digit, we can use the formula:
Percentage Difference = (Difference / Original Value) * 100
In this case, the difference is 9b - 8.55a, and the original value is 8.55a.
Percentage Difference = [(9b - 8.55a) / 8.55a] * 100
Step 7: Simplify the Equation
To simplify the equation, we can substitute the value of 8.55a from the previous equation:
Percentage Difference = [(9b - 8.55a) / 8.55a] * 100
= [(9b - 9b) / 8.55a] * 100
= 0
Therefore, the percentage difference between the units place digit and the tens place digit is 0%.
Conclusion:
The units place digit is not greater than the tens place digit as the percentage difference is 0%.
To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.