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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)58
- c)36
- d)76
Correct answer is '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
= 10(x+3)+x
∵ Two digit no = 10 * tens digit + unit digit
digits interchanged =10x + x + 3
⇒ 10 (x+3) + x + 10x + x + 3 =143
⇒ 10x + 30 + 12x + 3 = 143
⇒ 22x + 33 = 143
⇒ 22x = 143−33
⇒ 22x=110
⇒ x=110
⇒ x=5
Original number = 85
Most Upvoted Answer
The digits of a two-digit number differ by 3. If the digits are interc...
Given:
- 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.
To find:
- The possible original number.
Solution:
Let's assume the original number to be 10x + y, where x is the tens digit and y is the units digit.
Step 1: Determine the relationship between the digits:
The difference between the digits is given as 3. So, we can write the equation as:
x - y = 3 ...(Equation 1)
Step 2: Determine the new number formed by interchanging the digits:
When the digits are interchanged, the new number becomes 10y + x.
Step 3: Determine the sum of the original number and the new number:
The sum of the original number and the new number is given as 143. So, we can write the equation as:
(10x + y) + (10y + x) = 143
11x + 11y = 143
Dividing both sides by 11, we get:
x + y = 13 ...(Equation 2)
Step 4: Solve the system of equations:
We now have a system of two equations (Equation 1 and Equation 2) that we need to solve simultaneously to find the values of x and y.
By solving Equation 1 and Equation 2, we find that the values of x and y are 8 and 5 respectively.
Step 5: Determine the original number:
The original number is given by 10x + y = 10(8) + 5 = 85.
Therefore, the original number can be 85.
Hence, the correct answer is option A) 85.
- 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.
To find:
- The possible original number.
Solution:
Let's assume the original number to be 10x + y, where x is the tens digit and y is the units digit.
Step 1: Determine the relationship between the digits:
The difference between the digits is given as 3. So, we can write the equation as:
x - y = 3 ...(Equation 1)
Step 2: Determine the new number formed by interchanging the digits:
When the digits are interchanged, the new number becomes 10y + x.
Step 3: Determine the sum of the original number and the new number:
The sum of the original number and the new number is given as 143. So, we can write the equation as:
(10x + y) + (10y + x) = 143
11x + 11y = 143
Dividing both sides by 11, we get:
x + y = 13 ...(Equation 2)
Step 4: Solve the system of equations:
We now have a system of two equations (Equation 1 and Equation 2) that we need to solve simultaneously to find the values of x and y.
By solving Equation 1 and Equation 2, we find that the values of x and y are 8 and 5 respectively.
Step 5: Determine the original number:
The original number is given by 10x + y = 10(8) + 5 = 85.
Therefore, the original number can be 85.
Hence, the correct answer is option A) 85.
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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)58c)36d)76Correct answer is 'A'. Can you explain this answer?
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