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A number consists of three consecutive digits in order, the one in units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digits. Find the number.
- a)345
- b)567
- c)123
- d)234
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A number consists of three consecutive digits in order, the one in uni...
Let the digits at hundred's place be x.
Hence the number will have the digits as x, x + 1 and x + 2.
Number will be 100x + 10x + 10 + x + 2 = 111x + 12
Number obtained after reversing the digits = 100x + 200 + 10x + 10 + x = 111x + 210
Sum of the digits = x + x + 1 + x + 2 = 3x + 3
According to the question,
⇒ 111x + 210 = 111x + 12 + 22(3x + 3)
⇒ 210 = 12 + 66x + 66
⇒ 66x = 132
⇒ x = 2
Hence, the number will be 234.
Hence the number will have the digits as x, x + 1 and x + 2.
Number will be 100x + 10x + 10 + x + 2 = 111x + 12
Number obtained after reversing the digits = 100x + 200 + 10x + 10 + x = 111x + 210
Sum of the digits = x + x + 1 + x + 2 = 3x + 3
According to the question,
⇒ 111x + 210 = 111x + 12 + 22(3x + 3)
⇒ 210 = 12 + 66x + 66
⇒ 66x = 132
⇒ x = 2
Hence, the number will be 234.
Most Upvoted Answer
A number consists of three consecutive digits in order, the one in uni...
To solve this problem, let's break it down into steps:
Step 1: Understand the problem
We are given a number consisting of three consecutive digits, with the greatest digit in the units place. We need to find this number.
Step 2: Express the number algebraically
Let's express the number algebraically as 100a + 10b + c, where a, b, and c represent the hundreds, tens, and units digits, respectively.
Step 3: Reverse the digits of the number
To reverse the digits, we can express it as 100c + 10b + a.
Step 4: Set up the equation
According to the problem, the number formed by reversing the digits exceeds the original number by 22 times the sum of the digits. Mathematically, this can be expressed as:
(100c + 10b + a) - (100a + 10b + c) = 22(a + b + c)
Simplifying this equation, we get:
99c - 99a = 21(a + b + c)
Step 5: Simplify the equation
Dividing both sides of the equation by 3, we get:
33c - 33a = 7(a + b + c)
Further simplifying, we have:
33(c - a) = 7(a + b + c)
Step 6: Determine the possible values for a, b, and c
Since a, b, and c represent the hundreds, tens, and units digits, they can only take on the values 1, 2, 3, 4, 5, 6, 7, 8, or 9.
Step 7: Test the values
We can test each of the possible values for a, b, and c to see which one satisfies the equation.
If a = 1, b = 2, and c = 3, the equation becomes:
33(3 - 1) = 7(1 + 2 + 3)
66 = 7(6)
66 = 42 (False)
If a = 2, b = 3, and c = 4, the equation becomes:
33(4 - 2) = 7(2 + 3 + 4)
66 = 7(9)
66 = 63 (False)
If a = 3, b = 4, and c = 5, the equation becomes:
33(5 - 3) = 7(3 + 4 + 5)
66 = 7(12)
66 = 84 (False)
If a = 4, b = 5, and c = 6, the equation becomes:
33(6 - 4) = 7(4 + 5 + 6)
66 = 7(15)
66 = 105 (False)
If a = 5, b = 6, and c = 7, the equation becomes:
33(7 - 5) = 7(5 + 6 + 7)
66 = 7(18)
66 = 126 (False)
If a = 6, b = 7, and c = 8, the equation becomes:
33(8 - 6) = 7(6 + 7 + 8)
66 = 7(21)
Step 1: Understand the problem
We are given a number consisting of three consecutive digits, with the greatest digit in the units place. We need to find this number.
Step 2: Express the number algebraically
Let's express the number algebraically as 100a + 10b + c, where a, b, and c represent the hundreds, tens, and units digits, respectively.
Step 3: Reverse the digits of the number
To reverse the digits, we can express it as 100c + 10b + a.
Step 4: Set up the equation
According to the problem, the number formed by reversing the digits exceeds the original number by 22 times the sum of the digits. Mathematically, this can be expressed as:
(100c + 10b + a) - (100a + 10b + c) = 22(a + b + c)
Simplifying this equation, we get:
99c - 99a = 21(a + b + c)
Step 5: Simplify the equation
Dividing both sides of the equation by 3, we get:
33c - 33a = 7(a + b + c)
Further simplifying, we have:
33(c - a) = 7(a + b + c)
Step 6: Determine the possible values for a, b, and c
Since a, b, and c represent the hundreds, tens, and units digits, they can only take on the values 1, 2, 3, 4, 5, 6, 7, 8, or 9.
Step 7: Test the values
We can test each of the possible values for a, b, and c to see which one satisfies the equation.
If a = 1, b = 2, and c = 3, the equation becomes:
33(3 - 1) = 7(1 + 2 + 3)
66 = 7(6)
66 = 42 (False)
If a = 2, b = 3, and c = 4, the equation becomes:
33(4 - 2) = 7(2 + 3 + 4)
66 = 7(9)
66 = 63 (False)
If a = 3, b = 4, and c = 5, the equation becomes:
33(5 - 3) = 7(3 + 4 + 5)
66 = 7(12)
66 = 84 (False)
If a = 4, b = 5, and c = 6, the equation becomes:
33(6 - 4) = 7(4 + 5 + 6)
66 = 7(15)
66 = 105 (False)
If a = 5, b = 6, and c = 7, the equation becomes:
33(7 - 5) = 7(5 + 6 + 7)
66 = 7(18)
66 = 126 (False)
If a = 6, b = 7, and c = 8, the equation becomes:
33(8 - 6) = 7(6 + 7 + 8)
66 = 7(21)
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A number consists of three consecutive digits in order, the one in units place being the greatest of the three. The number formed by reversing the digits exceeds the original number by 22 times the sum of the digits. Find the number.a)345b)567c)123d)234Correct answer is option 'D'. Can you explain this answer?
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