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The sum of digits of a two-digit number is 13. When 45 is added to the number, the digits of the number are reversed. What is the actual number? (1) 31 (2) 85 (3) 94 (4) 58 (5) 49?
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The sum of digits of a two-digit number is 13. When 45 is added to the...
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The sum of digits of a two-digit number is 13. When 45 is added to the...

Understanding the Problem:
The problem states that the sum of the digits of a two-digit number is 13. When 45 is added to the number, the digits of the number are reversed. We need to find the actual number.

Approach:
Let's assume the two-digit number to be 10x + y, where x and y are the digits of the number.

Formulating Equations:
1. x + y = 13 (sum of the digits is 13)
2. 10x + y + 45 = 10y + x (when 45 is added, the digits are reversed)

Solving the Equations:
From equation 1, we get x = 13 - y
Substitute x in equation 2:
10(13 - y) + y + 45 = 10y + 13 - y
130 - 10y + y + 45 = 10y + 13 - y
130 + 45 = 10y + 13 - y
175 = 9y + 13
9y = 162
y = 18

Substitute y back into x + y = 13:
x + 18 = 13
x = -5

Since x and y are digits, x cannot be negative. Therefore, our assumption of x and y was incorrect.

Actual Number Calculation:
By trying the given options, we find that only option (5) 49 satisfies the conditions:
4 + 9 = 13
49 + 45 = 94 (digits reversed)

Therefore, the actual number is 49.
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Direction: Study the following information and answer the given question.Five of my friends Aman, Deepak, Isha, Priya and Shweta were trying to find my debit card PIN number, which was a 4-digit number. I gave them a clue that no digit was greater than 4 and there was no zero in the PIN. I offered Rs. 100 for the person who guessed the first digit right, Rs. 200, Rs. 300 and Rs. 400 for the person who correctly guessed the second, the third and the fourth digits, respectively. Actually, all the 4 digits of the PIN were different, but my friends did not know that. After some time, they told me their guesses, parts of which are given below:It is also known that:1. Priya guessed all the digits differently and earned the lowest amount. Deepak earned less than Shweta did.2. Deepak did not guess 2 or 4 for the first two digits, and he guessed two different digits.3. No two people guessed the same number of digits right.Q. How many people guessed all the four digits differently?

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The sum of digits of a two-digit number is 13. When 45 is added to the number, the digits of the number are reversed. What is the actual number? (1) 31 (2) 85 (3) 94 (4) 58 (5) 49?
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The sum of digits of a two-digit number is 13. When 45 is added to the number, the digits of the number are reversed. What is the actual number? (1) 31 (2) 85 (3) 94 (4) 58 (5) 49? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about The sum of digits of a two-digit number is 13. When 45 is added to the number, the digits of the number are reversed. What is the actual number? (1) 31 (2) 85 (3) 94 (4) 58 (5) 49? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of digits of a two-digit number is 13. When 45 is added to the number, the digits of the number are reversed. What is the actual number? (1) 31 (2) 85 (3) 94 (4) 58 (5) 49?.
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