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In a two digit number the digits differ by 2. ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90. find the number?
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In a two digit number the digits differ by 2. ten times the number exc...
Solution:
Given conditions:
- The digits of the number differ by 2.
- Ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90.
Let's assume the two-digit number is represented as 10x + y, where x and y are the tens and units digits respectively.
Difference between the digits:
- According to the given condition, the digits differ by 2. Therefore, we have x - y = 2 or x = y + 2.
Equation based on the given conditions:
- Ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90:
10(10x + y) = 5(10y + x) + x + y + 90
=> 100x + 10y = 50y + 5x + x + y + 90
=> 95x - 40y = 90
Substitute x = y + 2 into the equation:
95(y + 2) - 40y = 90
=> 95y + 190 - 40y = 90
=> 55y = -100
=> y = -100 / 55
=> y = -20/11 (not a valid digit)
Conclusion:
- Since y is not a valid digit, there is no two-digit number that satisfies the given conditions.
Given conditions:
- The digits of the number differ by 2.
- Ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90.
Let's assume the two-digit number is represented as 10x + y, where x and y are the tens and units digits respectively.
Difference between the digits:
- According to the given condition, the digits differ by 2. Therefore, we have x - y = 2 or x = y + 2.
Equation based on the given conditions:
- Ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90:
10(10x + y) = 5(10y + x) + x + y + 90
=> 100x + 10y = 50y + 5x + x + y + 90
=> 95x - 40y = 90
Substitute x = y + 2 into the equation:
95(y + 2) - 40y = 90
=> 95y + 190 - 40y = 90
=> 55y = -100
=> y = -100 / 55
=> y = -20/11 (not a valid digit)
Conclusion:
- Since y is not a valid digit, there is no two-digit number that satisfies the given conditions.
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In a two digit number the digits differ by 2. ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90. find the number?
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In a two digit number the digits differ by 2. ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90. find the number? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a two digit number the digits differ by 2. ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90. find the number? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a two digit number the digits differ by 2. ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90. find the number?.
In a two digit number the digits differ by 2. ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90. find the number? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a two digit number the digits differ by 2. ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90. find the number? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a two digit number the digits differ by 2. ten times the number exceeds 5 times the sum of the number formed by reversing its digits and the sum of its digits by 90. find the number?.
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