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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
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The sum of two digits and the number formed by interchanging its 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
The sum of two digits and the number formed by interchanging its digit...
To solve this problem, we can start by assigning variables to the digits in the number. Let's say the first digit is x and the second digit is y.
Given information:
1) The sum of the digits and the number formed by interchanging the digits is 110. This can be written as:
x + y + 10x + y = 110
11x + 2y = 110
2) 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. This can be written as:
10x - 10 = 5(x + y) + 4
10x - 10 = 5x + 5y + 4
5x - 5y = 14
Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.
Solving the system of equations:
1) Multiply the second equation by 2 to eliminate the y term:
10x - 10 = 10x + 10y + 8
-10y = 18
y = -18/10
y = -9/5
2) Substitute the value of y into the first equation:
11x + 2(-9/5) = 110
11x - 18/5 = 110
11x = 110 + 18/5
11x = 550/5 + 18/5
11x = 568/5
x = (568/5) / 11
x = 568/55
So, the first digit x is 568/55 and the second digit y is -9/5.
However, since we are dealing with digits, both x and y must be integers. We can test different values of x and see if they satisfy the given conditions.
Testing values of x:
Let's start with x = 5. If x = 5, then y = (110 - 11x)/2 = (110 - 11(5))/2 = 55/2 = 27.5, which is not an integer.
Next, let's try x = 6. If x = 6, then y = (110 - 11x)/2 = (110 - 11(6))/2 = 44/2 = 22. Here, both x and y are integers.
Therefore, the first number is 6, and the second number is 22. The correct answer is option C) 64.
Given information:
1) The sum of the digits and the number formed by interchanging the digits is 110. This can be written as:
x + y + 10x + y = 110
11x + 2y = 110
2) 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. This can be written as:
10x - 10 = 5(x + y) + 4
10x - 10 = 5x + 5y + 4
5x - 5y = 14
Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.
Solving the system of equations:
1) Multiply the second equation by 2 to eliminate the y term:
10x - 10 = 10x + 10y + 8
-10y = 18
y = -18/10
y = -9/5
2) Substitute the value of y into the first equation:
11x + 2(-9/5) = 110
11x - 18/5 = 110
11x = 110 + 18/5
11x = 550/5 + 18/5
11x = 568/5
x = (568/5) / 11
x = 568/55
So, the first digit x is 568/55 and the second digit y is -9/5.
However, since we are dealing with digits, both x and y must be integers. We can test different values of x and see if they satisfy the given conditions.
Testing values of x:
Let's start with x = 5. If x = 5, then y = (110 - 11x)/2 = (110 - 11(5))/2 = 55/2 = 27.5, which is not an integer.
Next, let's try x = 6. If x = 6, then y = (110 - 11x)/2 = (110 - 11(6))/2 = 44/2 = 22. Here, both x and y are integers.
Therefore, the first number is 6, and the second number is 22. The correct answer is option C) 64.
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