CAT Exam  >  CAT Questions  >  A number when reversed become 45% greater tha... Start Learning for Free
A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit?
Verified Answer
A number when reversed become 45% greater than the original. By how mu...
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
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%.
Attention CAT Students!
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.
Explore Courses for CAT exam

Similar CAT Doubts

A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit?
Question Description
A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit?.
Solutions for A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit? defined & explained in the simplest way possible. Besides giving the explanation of A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit?, a detailed solution for A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit? has been provided alongside types of A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit? theory, EduRev gives you an ample number of questions to practice A number when reversed become 45% greater than the original. By how much percentage is the unit s place digit greater than the ten s place digit? tests, examples and also practice CAT tests.
Explore Courses for CAT exam

Top Courses for CAT

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev