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The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?
- a)85
- b)92
- c)36
- d)76
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The digits of a two-digit number differ by 3. If the digits are interc...
Let the unit digit be x
Tens digit = x+3
Therefore, the number formed = 10(x+3)+x ∵ Two digit no = 10 * tens digit + unit digit
Tens digit = x+3
Therefore, the number formed = 10(x+3)+x ∵ Two digit no = 10 * tens digit + unit digit
When digits are interchanged i.e
Unit digit = x+3
Tens digit = x
Therefore, the number formed by interchanging the digits is
10x + x + 3
Now, According to question
Unit digit = x+3
Tens digit = x
Therefore, the number formed by interchanging the digits is
10x + x + 3
Now, According to question
⇒ 10 (x+3) + x + 10x + x + 3 =143
⇒ 10x + 30 + 12x + 3 = 143
⇒ 22x + 33 = 143
Transposing '33' to R.H.S, we get
22x = 143−33
⇒ 22x=110
Transposing '22' to L.H.S, we get
x=110/22
⇒ x=5
⇒ 10x + 30 + 12x + 3 = 143
⇒ 22x + 33 = 143
Transposing '33' to R.H.S, we get
22x = 143−33
⇒ 22x=110
Transposing '22' to L.H.S, we get
x=110/22
⇒ x=5
Therefore, Original number = 10(5+3) + 5 = 85
Most Upvoted Answer
The digits of a two-digit number differ by 3. If the digits are interc...
Problem: Find the original two-digit number if the digits differ by 3 and their sum equals 143.
Solution:
Let the tens digit be x and the units digit be y.
Then, the original two-digit number can be expressed as 10x + y.
According to the problem, the digits differ by 3. Therefore, we have two cases:
Case 1: x - y = 3
In this case, the two-digit number can be expressed as 10x + y, and the number obtained by interchanging the digits can be expressed as 10y + x. The sum of these two numbers is given as 143.
Therefore, we have the following equation:
10x + y + 10y + x = 143
Simplifying the above equation, we get:
11x + 11y = 143
Dividing both sides by 11, we get:
x + y = 13
Now, we need to find the values of x and y that satisfy both x - y = 3 and x + y = 13.
Solving the two equations simultaneously, we get x = 8 and y = 5.
Therefore, the original two-digit number is 10x + y = 85.
Case 2: y - x = 3
In this case, the two-digit number can be expressed as 10x + y, and the number obtained by interchanging the digits can be expressed as 10y + x. The sum of these two numbers is given as 143.
Therefore, we have the following equation:
10x + y + 10y + x = 143
Simplifying the above equation, we get:
11x + 11y = 143
Dividing both sides by 11, we get:
x + y = 13
Now, we need to find the values of x and y that satisfy both y - x = 3 and x + y = 13.
Solving the two equations simultaneously, we get x = 5/2 and y = 13/2, which are not whole numbers. Therefore, this case is not valid.
Therefore, the only possible answer is A, which is 85.
Solution:
Let the tens digit be x and the units digit be y.
Then, the original two-digit number can be expressed as 10x + y.
According to the problem, the digits differ by 3. Therefore, we have two cases:
Case 1: x - y = 3
In this case, the two-digit number can be expressed as 10x + y, and the number obtained by interchanging the digits can be expressed as 10y + x. The sum of these two numbers is given as 143.
Therefore, we have the following equation:
10x + y + 10y + x = 143
Simplifying the above equation, we get:
11x + 11y = 143
Dividing both sides by 11, we get:
x + y = 13
Now, we need to find the values of x and y that satisfy both x - y = 3 and x + y = 13.
Solving the two equations simultaneously, we get x = 8 and y = 5.
Therefore, the original two-digit number is 10x + y = 85.
Case 2: y - x = 3
In this case, the two-digit number can be expressed as 10x + y, and the number obtained by interchanging the digits can be expressed as 10y + x. The sum of these two numbers is given as 143.
Therefore, we have the following equation:
10x + y + 10y + x = 143
Simplifying the above equation, we get:
11x + 11y = 143
Dividing both sides by 11, we get:
x + y = 13
Now, we need to find the values of x and y that satisfy both y - x = 3 and x + y = 13.
Solving the two equations simultaneously, we get x = 5/2 and y = 13/2, which are not whole numbers. Therefore, this case is not valid.
Therefore, the only possible answer is A, which is 85.
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Community Answer
The digits of a two-digit number differ by 3. If the digits are interc...
Let the ones place= x let the tens place = x-3 no.= 10(x-3)+x =10x-30+x if we interchange the digit than new no. = (10×x)+x-3 =10x+x-3 =11x-30+11x-3=143 22x-30-3=143 =22x-33=143 22x=143+33 =22x=176 x=176÷22 =8, so the ones place no. is 8 therefore tens place no. is 8-3=5 so, the no. is 58
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The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?a)85b)92c)36d)76Correct answer is option 'A'. Can you explain this answer?
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The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?a)85b)92c)36d)76Correct answer is option 'A'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?a)85b)92c)36d)76Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. What can be the original number?a)85b)92c)36d)76Correct answer is option 'A'. Can you explain this answer?.
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