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The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.
Ans:
Let the ten's and unit digit be x and 8/x respectively.
Then,
⇒ 10x2 + 18x + 8 = 80 + x2
⇒ 10x2−x2 +18x + 8 − 80 = 0
⇒ 9x2 +18x − 72 = 0
⇒ x2 + 2x - 8 = 0
⇒ x2 + 4x − 2x − 8 = 0
⇒ x(x + 4) − 2(x + 4) = 0
⇒ x = −4, 2 ∴ x = 2sinθx > 0
⇒ 8/x = 8/2 = 4.
∴ The numbers is 24.?
Ans:
Let the ten's and unit digit be x and 8/x respectively.
Then,
⇒ 10x2 + 18x + 8 = 80 + x2
⇒ 10x2−x2 +18x + 8 − 80 = 0
⇒ 9x2 +18x − 72 = 0
⇒ x2 + 2x - 8 = 0
⇒ x2 + 4x − 2x − 8 = 0
⇒ x(x + 4) − 2(x + 4) = 0
⇒ x = −4, 2 ∴ x = 2sinθx > 0
⇒ 8/x = 8/2 = 4.
∴ The numbers is 24.?
Most Upvoted Answer
The sum of the digits of a 2-digit number is 8. When 18 is added to th...
Understanding the Problem
To solve the problem, we need to find a 2-digit number where:
- The sum of its digits equals 8.
- Adding 18 to the number reverses its digits.
Let's denote the ten's digit as "x" and the unit's digit as "y".
Setting Up the Equations
1. Sum of Digits:
- x + y = 8
2. Reversed Digits Condition:
- The original number can be represented as 10x + y.
- When 18 is added, we can express the reversed number as 10y + x.
- Therefore, we have:
(10x + y) + 18 = 10y + x
Rearranging the Equation
From the equation:
- 10x + y + 18 = 10y + x
Rearranging gives:
- 10x - x + y - 10y + 18 = 0
- 9x - 9y + 18 = 0
- Simplifying, we get:
x - y + 2 = 0
or
x - y = -2
(This means y = x + 2)
Substituting Values
Now we can substitute for y in our sum of digits equation:
- x + (x + 2) = 8
- 2x + 2 = 8
- 2x = 6
- x = 3
Using x to find y:
- y = x + 2 = 3 + 2 = 5
Finding the Number
Putting x and y together, the 2-digit number is:
- 10x + y = 10(3) + 5 = 35
Verification
- The sum of digits (3 + 5) equals 8.
- Adding 18: 35 + 18 = 53, which is indeed the reverse of 35.
Conclusion
The 2-digit number is 35.
To solve the problem, we need to find a 2-digit number where:
- The sum of its digits equals 8.
- Adding 18 to the number reverses its digits.
Let's denote the ten's digit as "x" and the unit's digit as "y".
Setting Up the Equations
1. Sum of Digits:
- x + y = 8
2. Reversed Digits Condition:
- The original number can be represented as 10x + y.
- When 18 is added, we can express the reversed number as 10y + x.
- Therefore, we have:
(10x + y) + 18 = 10y + x
Rearranging the Equation
From the equation:
- 10x + y + 18 = 10y + x
Rearranging gives:
- 10x - x + y - 10y + 18 = 0
- 9x - 9y + 18 = 0
- Simplifying, we get:
x - y + 2 = 0
or
x - y = -2
(This means y = x + 2)
Substituting Values
Now we can substitute for y in our sum of digits equation:
- x + (x + 2) = 8
- 2x + 2 = 8
- 2x = 6
- x = 3
Using x to find y:
- y = x + 2 = 3 + 2 = 5
Finding the Number
Putting x and y together, the 2-digit number is:
- 10x + y = 10(3) + 5 = 35
Verification
- The sum of digits (3 + 5) equals 8.
- Adding 18: 35 + 18 = 53, which is indeed the reverse of 35.
Conclusion
The 2-digit number is 35.
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The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.?
Question Description
The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.?.
The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.?.
Solutions for The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.? in English & in Hindi are available as part of our courses for Class 7.
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Here you can find the meaning of The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.? defined & explained in the simplest way possible. Besides giving the explanation of
The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.?, a detailed solution for The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.? has been provided alongside types of The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.? theory, EduRev gives you an
ample number of questions to practice The sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.Ans:Let the ten's and unit digit be x and 8/x respectively.Then, ⇒ 10x2 + 18x + 8 = 80 + x2⇒ 10x2−x2 +18x + 8 − 80 = 0⇒ 9x2 +18x − 72 = 0⇒ x2 + 2x - 8 = 0⇒ x2 + 4x − 2x − 8 = 0⇒ x(x + 4) − 2(x + 4) = 0⇒ x = −4, 2 ∴ x = 2sinθx > 0⇒ 8/x = 8/2 = 4.∴ The numbers is 24.? tests, examples and also practice Class 7 tests.
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