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Can you explain the answer of this question below:
The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.
- A:46
- B:48
- C:64
- D:84
The answer is c.
Most Upvoted Answer
Can you explain the answer of this question below:The sum of two digit...
Let the unit digit be y & tens digit be x.
Original number = (10x+y)
After interchanging the digits
New number = (10y+x)
(10x+y) + (10y+x) = 110
11x +11y = 110
11(x+y)= 110
x+y = 110/11
x+y= 10 (1)
x= 10-y (2)
(10x+y) - 10 = 4+ 5(x+y)
(10x+y) - 10 = 4+ 5(10)
(10x+y) = 4+ 50+10
(10x+y) = 64
10(10-y) +y = 64
100-10y +y= 64
100 -9y = 64
-9y = 64-100
-9y = -36
y= 36/9= 4
y= 4
putting the value of y in eqn 2
x= 10-y
x= 10-4
x= 6
Hence , the first number is 6 & second number is 4.
Original Number is 10x+y = 10* 6+4= 60+4= 64
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Community Answer
Can you explain the answer of this question below:The sum of two digit...
Given information:
- The sum of a two-digit number and the number formed by interchanging its digit is 110.
- If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number.
To find: The first number.
Solution:
Let the two-digit number be represented by 'xy' where x is the tens digit and y is the ones digit.
According to the first condition,
xy + yx = 110
=> 10x + y + 10y + x = 110
=> 11x + 11y = 110
=> x + y = 10
Now, let's consider the second condition.
If ten is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number.
=> 10x + y - 10 = 5(x + y) + 4
=> 10x + y - 5x - 5y = 14
=> 5x - 4y = 14
=> 5x = 4y + 14
=> x = (4/5)y + (14/5)
As x is a digit, it must be an integer. Therefore, y must be a multiple of 5.
Let's try different values of y to check which one satisfies both conditions.
- If y = 5, then x = 6. But 65 - 10 ≠ 4 + 5(6)
- If y = 0, then x = 2. But 20 - 10 ≠ 4 + 5(2)
- If y = 5, then x = 6. But 65 - 10 ≠ 4 + 5(6)
Hence, the only possible value for y is 4.
If y = 4, then x = 6.
Therefore, the first number is 64.
Answer: (c) 64.
- The sum of a two-digit number and the number formed by interchanging its digit is 110.
- If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number.
To find: The first number.
Solution:
Let the two-digit number be represented by 'xy' where x is the tens digit and y is the ones digit.
According to the first condition,
xy + yx = 110
=> 10x + y + 10y + x = 110
=> 11x + 11y = 110
=> x + y = 10
Now, let's consider the second condition.
If ten is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number.
=> 10x + y - 10 = 5(x + y) + 4
=> 10x + y - 5x - 5y = 14
=> 5x - 4y = 14
=> 5x = 4y + 14
=> x = (4/5)y + (14/5)
As x is a digit, it must be an integer. Therefore, y must be a multiple of 5.
Let's try different values of y to check which one satisfies both conditions.
- If y = 5, then x = 6. But 65 - 10 ≠ 4 + 5(6)
- If y = 0, then x = 2. But 20 - 10 ≠ 4 + 5(2)
- If y = 5, then x = 6. But 65 - 10 ≠ 4 + 5(6)
Hence, the only possible value for y is 4.
If y = 4, then x = 6.
Therefore, the first number is 64.
Answer: (c) 64.
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Can you explain the answer of this question below:The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.A:46B:48C:64D:84The answer is c. for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Can you explain the answer of this question below:The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.A:46B:48C:64D:84The answer is c. covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.A:46B:48C:64D:84The answer is c..
Can you explain the answer of this question below:The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.A:46B:48C:64D:84The answer is c. for Class 8 2025 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Can you explain the answer of this question below:The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.A:46B:48C:64D:84The answer is c. covers all topics & solutions for Class 8 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.A:46B:48C:64D:84The answer is c..
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Can you explain the answer of this question below:The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.A:46B:48C:64D:84The answer is c., a detailed solution for Can you explain the answer of this question below:The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.A:46B:48C:64D:84The answer is c. has been provided alongside types of Can you explain the answer of this question below:The sum of two digits and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.A:46B:48C:64D:84The answer is c. theory, EduRev gives you an
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